About: Double coset

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In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y.

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rdfs:label	Double coset (en) 이중 잉여류 (ko) 双陪集 (zh)
rdfs:comment	군론에서 이중 잉여류(二重剩餘類, 영어: double coset)는 주어진 두 부분군에 의하여 결정되는 동치 관계에 대한 동치류이다. (ko) 在数学领域, 群G中的 (H,K) 双陪集在G上的等价关系下是一个等价类, 其中 H K 是 G 的子群, G上的等价关系定义如下 x ~ y, 如果存在 h 属于 H , k 属于 K 满足 hxk = y. 每个双陪集具有形式 HxK, 并且 G 分割为自身的 (H, K) 双陪集; 双陪集中的每个元素, 都是 H 在 G 中的右陪集 Hy和 K 在 G 中的左陪集 zK 的组合. 一类重要的情形是 H = K, 这时有一类内积 HyH·HyH 是双陪集的一个并集. 在某些材料中, 例如有限群, 这可以作为相关的环的基. (zh) In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y. (en)
dcterms:subject	Group theory
Wikipage page ID	982771 (xsd:integer)
Wikipage revision ID	1091892155 (xsd:integer)
Link from a Wikipage to another Wikipage	Representation theory Non-commutative ring Homogeneous space Permutation Permutation matrix Index of a subgroup Group theory Convolution Coset Mathematics Gelfand pair Non-abelian group Normal subgroup Modular group Congruence subgroup Equivalence class Clifford–Klein form Commutative ring Commutator subgroup Functional analysis Subgroup 2-transitive group Topological group Disjoint sets Divisor Hecke algebra of a locally compact group Hecke operator Equivalence relation Number theory Ring (mathematics) Group (mathematics) Group action Abelian group Lagrange's theorem (group theory) Bijection Bilinear map Transposition (mathematics) Direct product of groups Disjoint union Free abelian group Coprime Group ring Group theory Induced representation Integer Integral Bruhat decomposition Orbit (group theory) Set (mathematics) Union (set theory) Symmetric group Restricted representation Upper triangular matrix Properly discontinuously Transitive group action Arithmetic subgroup Cauchy–Frobenius lemma Reductive Lie group dbr:Mackey's_decomposition_theorem
sameAs	Double coset Double coset Double coset Double coset Double coset Double coset
dbp:wikiPageUsesTemplate	dbt:Math dbt:Reflist
has abstract	In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y. The set of all double cosets is denoted by (en) 군론에서 이중 잉여류(二重剩餘類, 영어: double coset)는 주어진 두 부분군에 의하여 결정되는 동치 관계에 대한 동치류이다. (ko) 在数学领域, 群G中的 (H,K) 双陪集在G上的等价关系下是一个等价类, 其中 H K 是 G 的子群, G上的等价关系定义如下 x ~ y, 如果存在 h 属于 H , k 属于 K 满足 hxk = y. 每个双陪集具有形式 HxK, 并且 G 分割为自身的 (H, K) 双陪集; 双陪集中的每个元素, 都是 H 在 G 中的右陪集 Hy和 K 在 G 中的左陪集 zK 的组合. 一类重要的情形是 H = K, 这时有一类内积 HyH·HyH 是双陪集的一个并集. 在某些材料中, 例如有限群, 这可以作为相关的环的基. (zh)
prov:wasDerivedFrom	wikipedia-en:Double_coset?oldid=1091892155&ns=0
page length (characters) of wiki page	20781 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Double_coset
is Link from a Wikipage to another Wikipage of	Homogeneous space (B, N) pair Complexification (Lie group) Period mapping Clifford–Klein form Hecke algebra of a finite group Hecke operator Hanna Neumann conjecture Product of group subsets Artin transfer (group theory) Kazhdan–Lusztig polynomial Principal ideal theorem Differential geometry of surfaces Bruhat decomposition Shimura variety
is foaf:primaryTopic of	wikipedia-en:Double_coset

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