. . . . . "En math\u00E9matiques, un groupe fini est un groupe constitu\u00E9 d'un nombre fini d'\u00E9l\u00E9ments."@fr . "In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century. One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004."@en . . . . "\u5728\u6578\u5B78\u88E1\uFF0C\u6709\u9650\u7FA4\u662F\u6709\u8457\u6709\u9650\u591A\u500B\u5143\u7D20\u7684\u7FA4\u3002\u6709\u9650\u7FA4\u7406\u8AD6\u4E2D\u7684\u67D0\u4E9B\u90E8\u4EFD\u572820\u4E16\u7D00\u6709\u8457\u5F88\u6DF1\u7684\u7814\u7A76\uFF0C\u5C24\u5176\u662F\u5728\u5C40\u90E8\u5206\u6790\u548C\u53EF\u89E3\u7FA4\u8207\u51AA\u96F6\u7FA4\u7684\u7406\u8AD6\u4E2D\u3002\u671F\u671B\u6709\u500B\u5B8C\u6574\u7684\u7406\u8AD6\u662F\u592A\u904E\u706B\u4E86\uFF1A\u5176\u8907\u96DC\u6027\u6703\u96A8\u8457\u7FA4\u8B8A\u5F97\u8D8A\u5927\u6642\u800C\u8B8A\u5F97\u58D3\u5012\u6027\u5730\u5DE8\u5927\u3002 \u8F03\u5C11\u58D3\u5012\u6027\u5730\uFF0C\u4F46\u4ECD\u7136\u5F88\u6709\u8DA3\u7684\u662F\u5728\u6709\u9650\u57DF\u4E0A\u7684\u4E00\u4E9B\u8F03\u5C0F\u4E00\u822C\u7DDA\u6027\u7FA4\u3002\u7FA4\u8AD6\u5B78\u5BB6J. L. Alperin \uFF08\u9875\u9762\u5B58\u6863\u5907\u4EFD\uFF0C\u5B58\u4E8E\u4E92\u8054\u7F51\u6863\u6848\u9986\uFF09\u66FE\u5BEB\u904E\uFF1A\u300C\u6709\u9650\u7FA4\u7684\u5178\u578B\u4F8B\u5B50\u70BAGL(n,q)\uFF0D\u5728q\u500B\u5143\u7D20\u7684\u57DF\u4E0A\u7684n\u7DAD\u4E00\u822C\u7DDA\u6027\u7FA4\u3002\u5B78\u751F\u5728\u5B78\u6B64\u9818\u57DF\u6642\uFF0C\u82E5\u4EE5\u5176\u4ED6\u7684\u4F8B\u5B50\u4F86\u505A\u4ECB\u7D39\uFF0C\u5247\u53EF\u80FD\u6703\u88AB\u5B8C\u5168\u5730\u8AA4\u5C0E\u3002\uFF08Bulletin (New Series) of the American Mathematical Society, 10 (1984) 121\uFF09\u6B64\u985E\u578B\u6700\u5C0F\u7684\u7FA4GL(2,3)\u7684\u8A0E\u8AD6\uFF0C\u898BVisualizing GL(2,p) \uFF08\u9875\u9762\u5B58\u6863\u5907\u4EFD\uFF0C\u5B58\u4E8E\u4E92\u8054\u7F51\u6863\u6848\u9986\uFF09\u3002 \u6709\u9650\u7FA4\u548C\u5C0D\u7A31\u6709\u76F4\u63A5\u5730\u95DC\u63A5\uFF0C\u7576\u5176\u88AB\u9650\u5236\u5728\u6709\u9650\u500B\u8F49\u8B8A\u6642\u3002\u5176\u8B49\u660E\u70BA\uFF0C\u9023\u7E8C\u5C0D\u7A31\uFF0C\u5982\u674E\u7FA4\u4E2D\u7684\uFF0C\u4E5F\u6703\u5C0E\u81F4\u6709\u9650\u7FA4\uFF0C\u5982\u5916\u723E\u7FA4\u3002\u5728\u6B64\u4E00\u65B9\u9762\uFF0C\u6709\u9650\u7FA4\u548C\u5176\u6027\u8CEA\u5C07\u80FD\u5920\u7528\u5728\u5982\u7406\u8AD6\u7269\u7406\u554F\u984C\u7684\u91CD\u8981\u5730\u65B9\uFF0C\u5373\u4F7F\u5176\u7528\u9014\u5728\u4E00\u958B\u59CB\u4E26\u4E0D\u986F\u8457\u3002 \u6BCF\u4E00\u8CEA\u6578\u968E\u7684\u6709\u9650\u7FA4\u90FD\u662F\u5FAA\u74B0\u7FA4\u3002"@zh . "En matem\u00E0tiques, un grup finit \u00E9s un grup constitu\u00EFt per un nombre finit d'elements, \u00E9s a dir, que t\u00E9 cardinal finit."@ca . . . . "Em matem\u00E1tica e \u00E1lgebra abstrata, um grupo finito \u00E9 um grupo cujo conjunto subjacente G tem finitamente muitos elementos. Durante o s\u00E9culo XX, os matem\u00E1ticos investigaram alguns aspectos da teoria dos grupos finitos em grande profundidade, especialmente a teoria local dos grupos finitos, a teoria dos grupos sol\u00FAveis e grupos nilpotentes. A determina\u00E7\u00E3o completa da estrutura de todos os grupos finitos \u00E9 demais para ter a esperan\u00E7a de encontrar todas as estruturas poss\u00EDveis. No entanto, a classifica\u00E7\u00E3o dos grupos simples finitos foi conseguida, o que significa que as bases de constru\u00E7\u00E3o a partir do qual conclu\u00EDmos que todos os grupos finitos que podem ser constru\u00EDdos s\u00E3o agora conhecidos, uma vez que cada grupo finito tem uma composi\u00E7\u00E3o de s\u00E9rie. Durante a segunda metade do s\u00E9culo XX, os matem\u00E1ticos como Claude Chevalley e Robert Steinberg tamb\u00E9m aumentaram a compreens\u00E3o de an\u00E1logos finitos de grupos cl\u00E1ssicos, e de outros grupos relacionados. Uma fam\u00EDlia das fam\u00EDlia de grupos \u00E9 a dos grupos gerais lineares sobre corpo finito. Grupos finitos ocorrem frequentemente quando se considera a simetria dos objetos matem\u00E1ticos ou f\u00EDsicos, quando esses objetos admitem apenas um n\u00FAmero finito de estrutura de preserva\u00E7\u00E3o de transforma\u00E7\u00F5es. A teoria de grupos de Lie, que pode ser vista como lidando com , \u00E9 fortemente influenciada pelos grupos de Weyl associados. Estes s\u00E3o grupos finitos gerados por reflex\u00F5es que atuam em um espa\u00E7o euclidiano de dimens\u00E3o finita. As propriedades de grupos finitos podem assim desempenhar um papel em mat\u00E9rias como f\u00EDsica te\u00F3rica e qu\u00EDmica."@pt . . . . "Endliche Gruppen treten im mathematischen Teilgebiet der Gruppentheorie auf. Eine Gruppe hei\u00DFt endliche Gruppe, wenn eine endliche Menge ist, also eine endliche Anzahl von Elementen hat."@de . . . . . . "1962"^^ . "1963"^^ . . . . "Eindige groep"@nl . "Grup finit"@ca . . "Grup hingga"@in . . . "Em matem\u00E1tica e \u00E1lgebra abstrata, um grupo finito \u00E9 um grupo cujo conjunto subjacente G tem finitamente muitos elementos. Durante o s\u00E9culo XX, os matem\u00E1ticos investigaram alguns aspectos da teoria dos grupos finitos em grande profundidade, especialmente a teoria local dos grupos finitos, a teoria dos grupos sol\u00FAveis e grupos nilpotentes."@pt . "En matem\u00E1ticas y \u00E1lgebra abstracta, un grupo finito es un grupo cuyo conjunto fundamental G tiene un n\u00FAmero de elementos finito. Durante el siglo XX, los matem\u00E1ticos han investigado ciertos aspectos de la teor\u00EDa de grupos finitos en gran profundidad, especialmente la de grupos finitos, y la teor\u00EDa de grupos resolubles y grupos nilpotentes. Una completa determinaci\u00F3n de la estructura de todos los grupos finitos es demasiado ambiciosa; el n\u00FAmero de posibles estructuras pronto se convierte en abrumadora. Sin embargo, la se ha podido conseguir, lo que significa que los \u00ABbloques de construcci\u00F3n\u00BB con los cuales todos los grupos finitos pueden ser construidos se conoce ahora, ya que cada grupo finito tiene una serie de composici\u00F3n."@es . . . "\uC720\uD55C\uAD70(\u6709\u9650\u7FA4, \uC601\uC5B4: finite group)\uC740 \uC218\uD559\uC801 \uC5F0\uAD6C \uB300\uC0C1\uC758 \uC77C\uC885\uC73C\uB85C, \uAD70(\u7FA4)\uC774\uBA74\uC11C \uC720\uD55C\uAC1C\uC758 \uC6D0\uC18C\uB97C \uAC00\uC9C0\uB294 \uAC83\uC744 \uB9D0\uD55C\uB2E4. \uB300\uC218\uD559\uC758 \uD55C \uBD84\uC57C\uC774\uB2E4. \uC720\uD55C\uAD70\uC758 \uC5F0\uAD6C\uB294 \uAE4C\uB2E4\uB86D\uAE30\uB85C \uC815\uD3C9\uC774 \uB098 \uC788\uB2E4. 1960\uB144\uB300\uC5D0 \uC640 \uC874 G. \uD1B0\uD504\uC2A8\uC774 \uC99D\uBA85\uD55C \uB97C \uBC14\uD0D5\uC73C\uB85C \uBAA8\uB4E0 \uC720\uD55C\uB2E8\uC21C\uAD70\uB4E4\uC744 \uBD84\uB958\uD560 \uC218 \uC788\uC5C8\uC9C0\uB9CC, \uC5EC\uC804\uD788 \uB9CE\uC740 \uBB38\uC81C\uB4E4\uC774 \uD480\uB9AC\uC9C0 \uC54A\uACE0 \uB0A8\uC544\uC788\uB2E4."@ko . . . . . . . . "Grupo finito"@pt . . "Dalam aljabar abstrak, grup hingga adalah grup yang adalah hingga. Grup hingga sering kali muncul ketika mempertimbangkan kesimetrian benda-benda matematika atau fisik, ketika objek-objek itu hanya menerima transformasi pelestarian struktur dalam jumlah terbatas. Contoh penting dari grup hingga termasuk grup siklik dan grup permutasi. Studi tentang kelompok hingga telah menjadi bagian integral dari teori grup sejak ia muncul pada abad ke-19. Salah satu bidang studi utama adalah klasifikasi: klasifikasi grup sederhana hingga (grup tanpa nontrivial subgrup normal) diselesaikan pada tahun 2004."@in . "\u6570\u5B66\u304A\u3088\u3073\u62BD\u8C61\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u6709\u9650\u7FA4(\u3086\u3046\u3052\u3093\u3050\u3093\u3001\u82F1: finite group)\u3068\u306F\u53F0\u3068\u306A\u3063\u3066\u3044\u308B\u96C6\u5408G\u304C\u6709\u9650\u500B\u306E\u5143\u3057\u304B\u6301\u305F\u306A\u3044\u3088\u3046\u306A\u7FA4\u306E\u3053\u3068\u3067\u3042\u308B\u300220\u4E16\u7D00\u306E\u9593\u6570\u5B66\u8005\u306F\u3001\u7279\u306B\u6709\u9650\u7FA4\u306E\u3084\u3001\u53EF\u89E3\u7FA4\u3084\u51AA\u96F6\u7FA4 \u306E\u7406\u8AD6\u306A\u3069\u3068\u3044\u3063\u305F\u3001\u6709\u9650\u7FA4\u306E\u7406\u8AD6\u306E\u3055\u307E\u3056\u307E\u306A\u9762\u3092\u6DF1\u304F\u7814\u7A76\u3057\u3066\u3044\u305F\u3002\u5168\u3066\u306E\u6709\u9650\u7FA4\u306E\u69CB\u9020\u306E\u5B8C\u5168\u306A\u6C7A\u5B9A\u306F\u4F59\u308A\u306B\u9060\u5927\u306A\u76EE\u6A19\u3060\u3063\u305F: \u3042\u308A\u5F97\u308B\u69CB\u9020\u306E\u6570\u306F\u3059\u3050\u306B\u5727\u5012\u7684\u306B\u5927\u304D\u304F\u306A\u3063\u305F\u3002\u3057\u304B\u3057\u3001\u5358\u7D14\u7FA4\u306E\u5B8C\u5168\u306A\u5206\u985E\u3068\u3044\u3046\u76EE\u6A19\u306F\u9054\u6210\u3055\u308C\u305F\u3002\u3064\u307E\u308A\u4EFB\u610F\u306E\u6709\u9650\u7FA4\u306E\u300C\u7D44\u307F\u7ACB\u3066\u90E8\u54C1\u300D\u306F\u73FE\u5728\u3067\u306F\u5B8C\u5168\u306B\u77E5\u3089\u308C\u3066\u3044\u308B(\u4EFB\u610F\u306E\u6709\u9650\u7FA4\u306F\u7D44\u6210\u5217\u3092\u6301\u3064)\u3002 20\u4E16\u7D00\u306E\u5F8C\u534A\u306B\u306F\u3001\u30B7\u30E5\u30F4\u30A1\u30EC\u30FC\u3084\u3068\u3044\u3063\u305F\u6570\u5B66\u8005\u306B\u3088\u3063\u3066\u3084\u95A2\u9023\u3059\u308B\u7FA4\u306E\u6709\u9650\u985E\u4F3C\u306E\u7406\u89E3\u304C\u6DF1\u307E\u3063\u305F\u3002\u305D\u308C\u3089\u306E\u7FA4\u306E\u65CF\u306E\u4E00\u3064\u306B\u306F\u6709\u9650\u4F53\u4E0A\u306E\u4E00\u822C\u7DDA\u578B\u7FA4\u304C\u3042\u308B\u3002 \u6709\u9650\u7FA4\u306F\u3001\u3042\u308B\u6570\u5B66\u7684\u30FB\u7269\u7406\u7684\u5BFE\u8C61\u306E\u69CB\u9020\u3092\u4FDD\u3064\u5909\u63DB\u304C\u6709\u9650\u500B\u3057\u304B\u306A\u3044\u5834\u5408\u306B\u3001\u305D\u306E\u5BFE\u8C61\u306E\u5BFE\u79F0\u6027\u3092\u8003\u3048\u308B\u3068\u304D\u306B\u51FA\u3066\u6765\u308B\u7FA4\u3067\u3042\u308B\u3002\u4ED6\u65B9\u3067\u3001\"\"\u3092\u6271\u3063\u3066\u3044\u308B\u3088\u3046\u306B\u3082\u307F\u306A\u305B\u308B\u30EA\u30FC\u7FA4\u306E\u7406\u8AD6\u306F\u3001\u95A2\u9023\u3059\u308B\u30EF\u30A4\u30EB\u7FA4\u306E\u5F71\u97FF\u3092\u5F37\u304F\u53D7\u3051\u308B\u3002\u6709\u9650\u6B21\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u306B\u4F5C\u7528\u3059\u308B\u93E1\u6620\u306B\u3088\u3063\u3066\u751F\u6210\u3055\u308C\u308B\u6709\u9650\u7FA4\u3082\u5B58\u5728\u3059\u308B\u3002\u305D\u308C\u3086\u3048\u3001\u6709\u9650\u7FA4\u306E\u7279\u6027\u306F\u3001\u7406\u8AD6\u7269\u7406\u5B66\u3084\u5316\u5B66\u306A\u3069\u306E\u5206\u91CE\u3067\u5F79\u76EE\u3092\u6301\u3064\u3002"@ja . . "Thompson"@en . . . "\u0421\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0430 \u0433\u0440\u0443\u043F\u0430"@uk . . . . "In de groepentheorie, een onderdeel van de wiskunde, is een eindige groep een groep die een eindig aantal elementen heeft. Het aantal elementen van de groep wordt de orde van de groep genoemd. Sommige aspecten van de theorie van eindige groepen zijn in de twintigste eeuw in groot detail onderzocht, in het bijzonder de lokale theorie, en de theorie van de oplosbare groepen van de nilpotente groepen. Het is echter niet mogelijk de structuur van alle eindige groepen compleet te bepalen; daarvoor is het aantal mogelijke structuren te groot. Wel is men er in de twintigste eeuw in geslaagd een classificatie van eindige enkelvoudige groepen op te stellen. Deze eindige enkelvoudige groepen kunnen worden gezien als de bepaling van de \"bouwblokken\" voor alle eindige groepen, aangezien elke groep een bevat. Dankzij het werk van de wiskundigen Chevalley en Steinberg is het begrip van eindige analoga van klassieke groepen en daaraan gerelateerde groepen in het tweede deel van de twintigste eeuw sterk toegenomen. Een zo'n familie van groepen wordt gevormd door de algemene lineaire groepen over eindige lichamen/velden. De groepentheoreticus J. L. Alperin heeft hierover het volgende geschreven dat \"Het typische voorbeeld van een eindige groep is , de algemene lineaire groep van dimensies over een lichaam/veld met elementen. De student die aan de hand van andere voorbeelden kennis maakt met het onderwerp wordt misleid.\" Eindige groepen komen vaak naar voren bij beschouwing van de symmetrie van wiskundige of natuurkundige objecten, als deze objecten slechts een eindig aantal structuurbewarende transformaties toelaten. De theorie van de lie-groepen, die gezien kan worden als zich bezighoudend met \"continue symmetrie\", is sterk be\u00EFnvloed door de geassocieerde weyl-groepen. Dit zijn eindige groepen die worden gegenereerd door spiegelingen die aangrijpen op een eindigdimensionale euclidische ruimte. Eigenschappen van eindige groepen kunnen dus een rol spelen in onderwerpen als de theoretische natuurkunde."@nl . . . . . . . . "\u0421\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0430 \u0433\u0440\u0443\u043F\u0430 \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0443\u043F, \u0446\u0435 \u0433\u0440\u0443\u043F\u0430 \u0437\u0456 \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E\u044E \u043A\u0456\u043B\u044C\u043A\u0456\u0441\u0442\u044E \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432. \u0413\u0440\u0443\u043F\u043E\u044E \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0440\u0430\u0437\u043E\u043C \u0437 \u0431\u0456\u043D\u0430\u0440\u043D\u043E\u044E \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0454\u044E, \u044F\u043A\u0430 \u0430\u0441\u043E\u0446\u0456\u0430\u0442\u0438\u0432\u043D\u0430 \u0434\u043B\u044F \u0431\u0443\u0434\u044C-\u044F\u043A\u043E\u0433\u043E \u0432\u043F\u0440\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0430\u043D\u043E\u0433\u043E \u043D\u0430\u0431\u043E\u0440\u0443 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u043C\u043D\u043E\u0436\u0438\u043D\u0438."@uk . "\u0632\u0645\u0631\u0629 \u0645\u0646\u062A\u0647\u064A\u0629"@ar . . . . "\u0421\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0430 \u0433\u0440\u0443\u043F\u0430 \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0443\u043F, \u0446\u0435 \u0433\u0440\u0443\u043F\u0430 \u0437\u0456 \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E\u044E \u043A\u0456\u043B\u044C\u043A\u0456\u0441\u0442\u044E \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432. \u0413\u0440\u0443\u043F\u043E\u044E \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0440\u0430\u0437\u043E\u043C \u0437 \u0431\u0456\u043D\u0430\u0440\u043D\u043E\u044E \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0454\u044E, \u044F\u043A\u0430 \u0430\u0441\u043E\u0446\u0456\u0430\u0442\u0438\u0432\u043D\u0430 \u0434\u043B\u044F \u0431\u0443\u0434\u044C-\u044F\u043A\u043E\u0433\u043E \u0432\u043F\u0440\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0430\u043D\u043E\u0433\u043E \u043D\u0430\u0431\u043E\u0440\u0443 \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u043C\u043D\u043E\u0436\u0438\u043D\u0438."@uk . . . . . . "\u0641\u064A \u0627\u0644\u062C\u0628\u0631 \u0627\u0644\u062A\u062C\u0631\u064A\u062F\u064A \u0627\u0644\u0632\u0645\u0631\u0629 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Finite group)\u200F\u060C \u0647\u064A \u0643\u0644 \u0632\u0645\u0631\u0629 \u062A\u062D\u062A\u0648\u064A \u0639\u0644\u0649 \u0639\u062F\u062F \u0645\u062D\u062F\u0648\u062F \u0645\u0646 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 (\u0623\u0648 \u0639\u062F\u062F \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u0645\u0646\u062A\u0647\u064D)\u060C \u0648\u064A\u0645\u0643\u0646 \u0645\u0639\u0627\u0644\u062C\u0629 \u0627\u0644\u0632\u0645\u0631 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 \u0628\u0639\u0645\u0642 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0632\u0645\u0631 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 \u0648\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0632\u0645\u0631 \u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062D\u0644\u062D\u0644\u0629."@ar . . "In matematica un gruppo finito \u00E8 un gruppo costituito da un numero finito di elementi. Ogni gruppo finito di ordine primo \u00E8 un gruppo ciclico. I gruppi abeliani finiti sono caratterizzati da un teorema di rappresentazione peculiare. Alcuni aspetti della teoria dei gruppi finiti sono stati investigati in profondit\u00E0 nel XX secolo, in particolare quelli della e le teorie dei gruppi risolubili e dei gruppi nilpotenti. \u00C8 peraltro eccessivo sperare di disporre tra breve di una teoria completa: quando si studiano gruppi finiti di elevata cardinalit\u00E0 la complessit\u00E0 diventa schiacciante."@it . . . . . . "\u041A\u043E\u043D\u0435\u0447\u043D\u0430\u044F \u0433\u0440\u0443\u043F\u043F\u0430 \u0432 \u043E\u0431\u0449\u0435\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u2014 \u0433\u0440\u0443\u043F\u043F\u0430, \u0441\u043E\u0434\u0435\u0440\u0436\u0430\u0449\u0430\u044F \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 (\u044D\u0442\u043E \u0447\u0438\u0441\u043B\u043E \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0435\u0451 \u00AB\u043F\u043E\u0440\u044F\u0434\u043A\u043E\u043C\u00BB). \u0414\u0430\u043B\u0435\u0435 \u0433\u0440\u0443\u043F\u043F\u0430 \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u0430\u0433\u0430\u0435\u0442\u0441\u044F \u043C\u0443\u043B\u044C\u0442\u0438\u043F\u043B\u0438\u043A\u0430\u0442\u0438\u0432\u043D\u043E\u0439, \u0442\u043E \u0435\u0441\u0442\u044C \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F \u0432 \u043D\u0435\u0439 \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442\u0441\u044F \u043A\u0430\u043A \u0443\u043C\u043D\u043E\u0436\u0435\u043D\u0438\u0435; \u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043D\u044B\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u0441 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u0435\u0439 \u0441\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043E\u0433\u043E\u0432\u0430\u0440\u0438\u0432\u0430\u044E\u0442\u0441\u044F \u043E\u0441\u043E\u0431\u043E. \u0415\u0434\u0438\u043D\u0438\u0446\u0443 \u043C\u0443\u043B\u044C\u0442\u0438\u043F\u043B\u0438\u043A\u0430\u0442\u0438\u0432\u043D\u043E\u0439 \u0433\u0440\u0443\u043F\u043F\u044B \u0431\u0443\u0434\u0435\u043C \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0442\u044C \u0441\u0438\u043C\u0432\u043E\u043B\u043E\u043C 1. \u041F\u043E\u0440\u044F\u0434\u043E\u043A \u0433\u0440\u0443\u043F\u043F\u044B \u043F\u0440\u0438\u043D\u044F\u0442\u043E \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0442\u044C \u041A\u043E\u043D\u0435\u0447\u043D\u044B\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u0448\u0438\u0440\u043E\u043A\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u044E\u0442\u0441\u044F \u043A\u0430\u043A \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435, \u0442\u0430\u043A \u0438 \u0432 \u0434\u0440\u0443\u0433\u0438\u0445 \u043D\u0430\u0443\u043A\u0430\u0445: \u043A\u0440\u0438\u043F\u0442\u043E\u0433\u0440\u0430\u0444\u0438\u044F, \u043A\u0440\u0438\u0441\u0442\u0430\u043B\u043B\u043E\u0433\u0440\u0430\u0444\u0438\u044F, \u0430\u0442\u043E\u043C\u043D\u0430\u044F \u0444\u0438\u0437\u0438\u043A\u0430, \u0442\u0435\u043E\u0440\u0438\u044F \u043E\u0440\u043D\u0430\u043C\u0435\u043D\u0442\u043E\u0432 \u0438 \u0434\u0440. \u041A\u043E\u043D\u0435\u0447\u043D\u044B\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0439 \u0442\u0435\u0441\u043D\u043E \u0441\u0432\u044F\u0437\u0430\u043D\u044B \u0441 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0435\u0439 \u0438\u0441\u0441\u043B\u0435\u0434\u0443\u0435\u043C\u044B\u0445 \u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432."@ru . . "\u0641\u064A \u0627\u0644\u062C\u0628\u0631 \u0627\u0644\u062A\u062C\u0631\u064A\u062F\u064A \u0627\u0644\u0632\u0645\u0631\u0629 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Finite group)\u200F\u060C \u0647\u064A \u0643\u0644 \u0632\u0645\u0631\u0629 \u062A\u062D\u062A\u0648\u064A \u0639\u0644\u0649 \u0639\u062F\u062F \u0645\u062D\u062F\u0648\u062F \u0645\u0646 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 (\u0623\u0648 \u0639\u062F\u062F \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u0645\u0646\u062A\u0647\u064D)\u060C \u0648\u064A\u0645\u0643\u0646 \u0645\u0639\u0627\u0644\u062C\u0629 \u0627\u0644\u0632\u0645\u0631 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 \u0628\u0639\u0645\u0642 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0632\u0645\u0631 \u0627\u0644\u0645\u0646\u062A\u0647\u064A\u0629 \u0648\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0632\u0645\u0631 \u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062D\u0644\u062D\u0644\u0629."@ar . . . . "En matem\u00E1ticas y \u00E1lgebra abstracta, un grupo finito es un grupo cuyo conjunto fundamental G tiene un n\u00FAmero de elementos finito. Durante el siglo XX, los matem\u00E1ticos han investigado ciertos aspectos de la teor\u00EDa de grupos finitos en gran profundidad, especialmente la de grupos finitos, y la teor\u00EDa de grupos resolubles y grupos nilpotentes. Una completa determinaci\u00F3n de la estructura de todos los grupos finitos es demasiado ambiciosa; el n\u00FAmero de posibles estructuras pronto se convierte en abrumadora. Sin embargo, la se ha podido conseguir, lo que significa que los \u00ABbloques de construcci\u00F3n\u00BB con los cuales todos los grupos finitos pueden ser construidos se conoce ahora, ya que cada grupo finito tiene una serie de composici\u00F3n. Durante la mitad del siglo XX, matem\u00E1ticos tales como y tambi\u00E9n incrementaron el entendimiento de los an\u00E1logos finitos de los grupos cl\u00E1sicos, y otros grupos relacionados. Una de estas familias de grupos es la familia de los grupos generales lineales sobre cuerpos finitos. Los grupos finitos tambi\u00E9n surgen cuando se considera la simetr\u00EDa de objetos matem\u00E1ticos o f\u00EDsicos, cuando esos objetos admiten s\u00F3lo un n\u00FAmero finito de transformaciones que preservan la estructura. La teor\u00EDa de los grupos de Lie,que puede ser vista como un trato con la \u00AB\u00BB, est\u00E1 fuertemente influenciada por los asociados. Hay grupos finitos generados por reflexiones que act\u00FAan sobre un espacio eucl\u00EDdeo de dimensi\u00F3n finita. Las propiedades de los grupos finitos pueden as\u00ED desempe\u00F1ar un papel importante en \u00E1reas como la f\u00EDsica te\u00F3rica y qu\u00EDmica."@es . . "\u6709\u9650\u7FA4"@zh . . . "In matematica un gruppo finito \u00E8 un gruppo costituito da un numero finito di elementi. Ogni gruppo finito di ordine primo \u00E8 un gruppo ciclico. I gruppi abeliani finiti sono caratterizzati da un teorema di rappresentazione peculiare. Alcuni aspetti della teoria dei gruppi finiti sono stati investigati in profondit\u00E0 nel XX secolo, in particolare quelli della e le teorie dei gruppi risolubili e dei gruppi nilpotenti. \u00C8 peraltro eccessivo sperare di disporre tra breve di una teoria completa: quando si studiano gruppi finiti di elevata cardinalit\u00E0 la complessit\u00E0 diventa schiacciante. Meno schiaccianti, ma ancora di grande interesse sono alcuni dei gruppi lineari generali sopra campi finiti di cardinalit\u00E0 contenute. Il teorico dei gruppi J. L. Alperin ha scritto che \"L'esempio tipico di gruppo finito \u00E8 GL(n,q), il gruppo lineare generale in n dimensioni sul campo di q elementi. Lo studente che fosse introdotto a questo settore con altri esempi sarebbe completamente fuorviato.\" (Bulletin (New Series) of the American Mathematical Society, 10 (1984) 121). Per una discussione di uno dei gruppi di questo genere pi\u00F9 piccoli, GL(2,3), vedi Visualizing GL(2,p). I gruppi finiti presentano un'utilit\u00E0 diretta per le questioni di simmetria limitate a insiemi finiti di trasformazioni. Accade che anche la simmetria continua, da trattare con i gruppi di Lie, si riconduce a gruppi finiti, i . Attraverso questa strada i gruppi finiti e le loro propriet\u00E0 possono assumere ruoli centrali in questioni nelle quali il loro ruolo a prima vista appare tutt'altro che ovvio, per esempio in varie problematiche della fisica teorica."@it . . . . . . "In de groepentheorie, een onderdeel van de wiskunde, is een eindige groep een groep die een eindig aantal elementen heeft. Het aantal elementen van de groep wordt de orde van de groep genoemd. Sommige aspecten van de theorie van eindige groepen zijn in de twintigste eeuw in groot detail onderzocht, in het bijzonder de lokale theorie, en de theorie van de oplosbare groepen van de nilpotente groepen. Het is echter niet mogelijk de structuur van alle eindige groepen compleet te bepalen; daarvoor is het aantal mogelijke structuren te groot. Wel is men er in de twintigste eeuw in geslaagd een classificatie van eindige enkelvoudige groepen op te stellen. Deze eindige enkelvoudige groepen kunnen worden gezien als de bepaling van de \"bouwblokken\" voor alle eindige groepen, aangezien elke groep een"@nl . . . . "\u041A\u043E\u043D\u0435\u0447\u043D\u0430\u044F \u0433\u0440\u0443\u043F\u043F\u0430 \u0432 \u043E\u0431\u0449\u0435\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u2014 \u0433\u0440\u0443\u043F\u043F\u0430, \u0441\u043E\u0434\u0435\u0440\u0436\u0430\u0449\u0430\u044F \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0435 \u0447\u0438\u0441\u043B\u043E \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 (\u044D\u0442\u043E \u0447\u0438\u0441\u043B\u043E \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0435\u0451 \u00AB\u043F\u043E\u0440\u044F\u0434\u043A\u043E\u043C\u00BB). \u0414\u0430\u043B\u0435\u0435 \u0433\u0440\u0443\u043F\u043F\u0430 \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u0430\u0433\u0430\u0435\u0442\u0441\u044F \u043C\u0443\u043B\u044C\u0442\u0438\u043F\u043B\u0438\u043A\u0430\u0442\u0438\u0432\u043D\u043E\u0439, \u0442\u043E \u0435\u0441\u0442\u044C \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044F \u0432 \u043D\u0435\u0439 \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442\u0441\u044F \u043A\u0430\u043A \u0443\u043C\u043D\u043E\u0436\u0435\u043D\u0438\u0435; \u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043D\u044B\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u0441 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u0435\u0439 \u0441\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043E\u0433\u043E\u0432\u0430\u0440\u0438\u0432\u0430\u044E\u0442\u0441\u044F \u043E\u0441\u043E\u0431\u043E. \u0415\u0434\u0438\u043D\u0438\u0446\u0443 \u043C\u0443\u043B\u044C\u0442\u0438\u043F\u043B\u0438\u043A\u0430\u0442\u0438\u0432\u043D\u043E\u0439 \u0433\u0440\u0443\u043F\u043F\u044B \u0431\u0443\u0434\u0435\u043C \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0442\u044C \u0441\u0438\u043C\u0432\u043E\u043B\u043E\u043C 1. \u041F\u043E\u0440\u044F\u0434\u043E\u043A \u0433\u0440\u0443\u043F\u043F\u044B \u043F\u0440\u0438\u043D\u044F\u0442\u043E \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0442\u044C \u041A\u043E\u043D\u0435\u0447\u043D\u044B\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u0448\u0438\u0440\u043E\u043A\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u044E\u0442\u0441\u044F \u043A\u0430\u043A \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435, \u0442\u0430\u043A \u0438 \u0432 \u0434\u0440\u0443\u0433\u0438\u0445 \u043D\u0430\u0443\u043A\u0430\u0445: \u043A\u0440\u0438\u043F\u0442\u043E\u0433\u0440\u0430\u0444\u0438\u044F, \u043A\u0440\u0438\u0441\u0442\u0430\u043B\u043B\u043E\u0433\u0440\u0430\u0444\u0438\u044F, \u0430\u0442\u043E\u043C\u043D\u0430\u044F \u0444\u0438\u0437\u0438\u043A\u0430, \u0442\u0435\u043E\u0440\u0438\u044F \u043E\u0440\u043D\u0430\u043C\u0435\u043D\u0442\u043E\u0432 \u0438 \u0434\u0440. \u041A\u043E\u043D\u0435\u0447\u043D\u044B\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0439 \u0442\u0435\u0441\u043D\u043E \u0441\u0432\u044F\u0437\u0430\u043D\u044B \u0441 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0435\u0439 \u0438\u0441\u0441\u043B\u0435\u0434\u0443\u0435\u043C\u044B\u0445 \u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432."@ru . . "yes"@en . "\uC720\uD55C\uAD70(\u6709\u9650\u7FA4, \uC601\uC5B4: finite group)\uC740 \uC218\uD559\uC801 \uC5F0\uAD6C \uB300\uC0C1\uC758 \uC77C\uC885\uC73C\uB85C, \uAD70(\u7FA4)\uC774\uBA74\uC11C \uC720\uD55C\uAC1C\uC758 \uC6D0\uC18C\uB97C \uAC00\uC9C0\uB294 \uAC83\uC744 \uB9D0\uD55C\uB2E4. \uB300\uC218\uD559\uC758 \uD55C \uBD84\uC57C\uC774\uB2E4. \uC720\uD55C\uAD70\uC758 \uC5F0\uAD6C\uB294 \uAE4C\uB2E4\uB86D\uAE30\uB85C \uC815\uD3C9\uC774 \uB098 \uC788\uB2E4. 1960\uB144\uB300\uC5D0 \uC640 \uC874 G. \uD1B0\uD504\uC2A8\uC774 \uC99D\uBA85\uD55C \uB97C \uBC14\uD0D5\uC73C\uB85C \uBAA8\uB4E0 \uC720\uD55C\uB2E8\uC21C\uAD70\uB4E4\uC744 \uBD84\uB958\uD560 \uC218 \uC788\uC5C8\uC9C0\uB9CC, \uC5EC\uC804\uD788 \uB9CE\uC740 \uBB38\uC81C\uB4E4\uC774 \uD480\uB9AC\uC9C0 \uC54A\uACE0 \uB0A8\uC544\uC788\uB2E4."@ko . . . . "Gruppo finito"@it . . . . . . . . . "Grupo finito"@es . . "\u6709\u9650\u7FA4"@ja . . . "Walter"@en . . . "15743"^^ . . "\u041A\u043E\u043D\u0435\u0447\u043D\u0430\u044F \u0433\u0440\u0443\u043F\u043F\u0430"@ru . . . . . . . . "Endliche Gruppen treten im mathematischen Teilgebiet der Gruppentheorie auf. Eine Gruppe hei\u00DFt endliche Gruppe, wenn eine endliche Menge ist, also eine endliche Anzahl von Elementen hat."@de . . "John Griggs Thompson"@en . . . . . . . . "En matem\u00E0tiques, un grup finit \u00E9s un grup constitu\u00EFt per un nombre finit d'elements, \u00E9s a dir, que t\u00E9 cardinal finit."@ca . . . . . "Walter Feit"@en . . "1111484283"^^ . . . . . . . . . . "323707"^^ . "Feit"@en . . . "En math\u00E9matiques, un groupe fini est un groupe constitu\u00E9 d'un nombre fini d'\u00E9l\u00E9ments."@fr . . "Endliche Gruppe"@de . . . . . "John Griggs"@en . . . . . "\u5728\u6578\u5B78\u88E1\uFF0C\u6709\u9650\u7FA4\u662F\u6709\u8457\u6709\u9650\u591A\u500B\u5143\u7D20\u7684\u7FA4\u3002\u6709\u9650\u7FA4\u7406\u8AD6\u4E2D\u7684\u67D0\u4E9B\u90E8\u4EFD\u572820\u4E16\u7D00\u6709\u8457\u5F88\u6DF1\u7684\u7814\u7A76\uFF0C\u5C24\u5176\u662F\u5728\u5C40\u90E8\u5206\u6790\u548C\u53EF\u89E3\u7FA4\u8207\u51AA\u96F6\u7FA4\u7684\u7406\u8AD6\u4E2D\u3002\u671F\u671B\u6709\u500B\u5B8C\u6574\u7684\u7406\u8AD6\u662F\u592A\u904E\u706B\u4E86\uFF1A\u5176\u8907\u96DC\u6027\u6703\u96A8\u8457\u7FA4\u8B8A\u5F97\u8D8A\u5927\u6642\u800C\u8B8A\u5F97\u58D3\u5012\u6027\u5730\u5DE8\u5927\u3002 \u8F03\u5C11\u58D3\u5012\u6027\u5730\uFF0C\u4F46\u4ECD\u7136\u5F88\u6709\u8DA3\u7684\u662F\u5728\u6709\u9650\u57DF\u4E0A\u7684\u4E00\u4E9B\u8F03\u5C0F\u4E00\u822C\u7DDA\u6027\u7FA4\u3002\u7FA4\u8AD6\u5B78\u5BB6J. L. Alperin \uFF08\u9875\u9762\u5B58\u6863\u5907\u4EFD\uFF0C\u5B58\u4E8E\u4E92\u8054\u7F51\u6863\u6848\u9986\uFF09\u66FE\u5BEB\u904E\uFF1A\u300C\u6709\u9650\u7FA4\u7684\u5178\u578B\u4F8B\u5B50\u70BAGL(n,q)\uFF0D\u5728q\u500B\u5143\u7D20\u7684\u57DF\u4E0A\u7684n\u7DAD\u4E00\u822C\u7DDA\u6027\u7FA4\u3002\u5B78\u751F\u5728\u5B78\u6B64\u9818\u57DF\u6642\uFF0C\u82E5\u4EE5\u5176\u4ED6\u7684\u4F8B\u5B50\u4F86\u505A\u4ECB\u7D39\uFF0C\u5247\u53EF\u80FD\u6703\u88AB\u5B8C\u5168\u5730\u8AA4\u5C0E\u3002\uFF08Bulletin (New Series) of the American Mathematical Society, 10 (1984) 121\uFF09\u6B64\u985E\u578B\u6700\u5C0F\u7684\u7FA4GL(2,3)\u7684\u8A0E\u8AD6\uFF0C\u898BVisualizing GL(2,p) \uFF08\u9875\u9762\u5B58\u6863\u5907\u4EFD\uFF0C\u5B58\u4E8E\u4E92\u8054\u7F51\u6863\u6848\u9986\uFF09\u3002 \u6709\u9650\u7FA4\u548C\u5C0D\u7A31\u6709\u76F4\u63A5\u5730\u95DC\u63A5\uFF0C\u7576\u5176\u88AB\u9650\u5236\u5728\u6709\u9650\u500B\u8F49\u8B8A\u6642\u3002\u5176\u8B49\u660E\u70BA\uFF0C\u9023\u7E8C\u5C0D\u7A31\uFF0C\u5982\u674E\u7FA4\u4E2D\u7684\uFF0C\u4E5F\u6703\u5C0E\u81F4\u6709\u9650\u7FA4\uFF0C\u5982\u5916\u723E\u7FA4\u3002\u5728\u6B64\u4E00\u65B9\u9762\uFF0C\u6709\u9650\u7FA4\u548C\u5176\u6027\u8CEA\u5C07\u80FD\u5920\u7528\u5728\u5982\u7406\u8AD6\u7269\u7406\u554F\u984C\u7684\u91CD\u8981\u5730\u65B9\uFF0C\u5373\u4F7F\u5176\u7528\u9014\u5728\u4E00\u958B\u59CB\u4E26\u4E0D\u986F\u8457\u3002 \u6BCF\u4E00\u8CEA\u6578\u968E\u7684\u6709\u9650\u7FA4\u90FD\u662F\u5FAA\u74B0\u7FA4\u3002"@zh . . . . "In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century. One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004."@en . . . . . . "Groupe fini"@fr . . . . . . "\uC720\uD55C\uAD70"@ko . . . . . . "\u6570\u5B66\u304A\u3088\u3073\u62BD\u8C61\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u6709\u9650\u7FA4(\u3086\u3046\u3052\u3093\u3050\u3093\u3001\u82F1: finite group)\u3068\u306F\u53F0\u3068\u306A\u3063\u3066\u3044\u308B\u96C6\u5408G\u304C\u6709\u9650\u500B\u306E\u5143\u3057\u304B\u6301\u305F\u306A\u3044\u3088\u3046\u306A\u7FA4\u306E\u3053\u3068\u3067\u3042\u308B\u300220\u4E16\u7D00\u306E\u9593\u6570\u5B66\u8005\u306F\u3001\u7279\u306B\u6709\u9650\u7FA4\u306E\u3084\u3001\u53EF\u89E3\u7FA4\u3084\u51AA\u96F6\u7FA4 \u306E\u7406\u8AD6\u306A\u3069\u3068\u3044\u3063\u305F\u3001\u6709\u9650\u7FA4\u306E\u7406\u8AD6\u306E\u3055\u307E\u3056\u307E\u306A\u9762\u3092\u6DF1\u304F\u7814\u7A76\u3057\u3066\u3044\u305F\u3002\u5168\u3066\u306E\u6709\u9650\u7FA4\u306E\u69CB\u9020\u306E\u5B8C\u5168\u306A\u6C7A\u5B9A\u306F\u4F59\u308A\u306B\u9060\u5927\u306A\u76EE\u6A19\u3060\u3063\u305F: \u3042\u308A\u5F97\u308B\u69CB\u9020\u306E\u6570\u306F\u3059\u3050\u306B\u5727\u5012\u7684\u306B\u5927\u304D\u304F\u306A\u3063\u305F\u3002\u3057\u304B\u3057\u3001\u5358\u7D14\u7FA4\u306E\u5B8C\u5168\u306A\u5206\u985E\u3068\u3044\u3046\u76EE\u6A19\u306F\u9054\u6210\u3055\u308C\u305F\u3002\u3064\u307E\u308A\u4EFB\u610F\u306E\u6709\u9650\u7FA4\u306E\u300C\u7D44\u307F\u7ACB\u3066\u90E8\u54C1\u300D\u306F\u73FE\u5728\u3067\u306F\u5B8C\u5168\u306B\u77E5\u3089\u308C\u3066\u3044\u308B(\u4EFB\u610F\u306E\u6709\u9650\u7FA4\u306F\u7D44\u6210\u5217\u3092\u6301\u3064)\u3002 20\u4E16\u7D00\u306E\u5F8C\u534A\u306B\u306F\u3001\u30B7\u30E5\u30F4\u30A1\u30EC\u30FC\u3084\u3068\u3044\u3063\u305F\u6570\u5B66\u8005\u306B\u3088\u3063\u3066\u3084\u95A2\u9023\u3059\u308B\u7FA4\u306E\u6709\u9650\u985E\u4F3C\u306E\u7406\u89E3\u304C\u6DF1\u307E\u3063\u305F\u3002\u305D\u308C\u3089\u306E\u7FA4\u306E\u65CF\u306E\u4E00\u3064\u306B\u306F\u6709\u9650\u4F53\u4E0A\u306E\u4E00\u822C\u7DDA\u578B\u7FA4\u304C\u3042\u308B\u3002 \u6709\u9650\u7FA4\u306F\u3001\u3042\u308B\u6570\u5B66\u7684\u30FB\u7269\u7406\u7684\u5BFE\u8C61\u306E\u69CB\u9020\u3092\u4FDD\u3064\u5909\u63DB\u304C\u6709\u9650\u500B\u3057\u304B\u306A\u3044\u5834\u5408\u306B\u3001\u305D\u306E\u5BFE\u8C61\u306E\u5BFE\u79F0\u6027\u3092\u8003\u3048\u308B\u3068\u304D\u306B\u51FA\u3066\u6765\u308B\u7FA4\u3067\u3042\u308B\u3002\u4ED6\u65B9\u3067\u3001\"\"\u3092\u6271\u3063\u3066\u3044\u308B\u3088\u3046\u306B\u3082\u307F\u306A\u305B\u308B\u30EA\u30FC\u7FA4\u306E\u7406\u8AD6\u306F\u3001\u95A2\u9023\u3059\u308B\u30EF\u30A4\u30EB\u7FA4\u306E\u5F71\u97FF\u3092\u5F37\u304F\u53D7\u3051\u308B\u3002\u6709\u9650\u6B21\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u306B\u4F5C\u7528\u3059\u308B\u93E1\u6620\u306B\u3088\u3063\u3066\u751F\u6210\u3055\u308C\u308B\u6709\u9650\u7FA4\u3082\u5B58\u5728\u3059\u308B\u3002\u305D\u308C\u3086\u3048\u3001\u6709\u9650\u7FA4\u306E\u7279\u6027\u306F\u3001\u7406\u8AD6\u7269\u7406\u5B66\u3084\u5316\u5B66\u306A\u3069\u306E\u5206\u91CE\u3067\u5F79\u76EE\u3092\u6301\u3064\u3002"@ja . . . "Finite group"@en . . . . . "Dalam aljabar abstrak, grup hingga adalah grup yang adalah hingga. Grup hingga sering kali muncul ketika mempertimbangkan kesimetrian benda-benda matematika atau fisik, ketika objek-objek itu hanya menerima transformasi pelestarian struktur dalam jumlah terbatas. Contoh penting dari grup hingga termasuk grup siklik dan grup permutasi."@in .