About: Schur multiplier

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In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by Issai Schur in his work on projective representations.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Group100031264 chemical compound yago:WikicatFiniteGroups
rdfs:label	Multiplicateur de Schur (fr) Schur multiplier (en) Мультипликатор Шура (ru)
rdfs:comment	In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by Issai Schur in his work on projective representations. (en) Мультипликатор Шура является второй группы G. Его ввёл Исай Шур в работе по проективным представлениям. (ru) En mathématiques, plus précisément en théorie des groupes, le multiplicateur de Schur est le deuxième groupe d'homologie d'un groupe G à coefficients entiers, . Si le groupe est présenté en termes d'un groupe libre F sur un ensemble de générateurs, et d'un sous-groupe normal R engendré par un ensemble de relations sur les générateurs, de sorte que , alors, par la formule d'homologie entière de Hopf, le multiplicateur de Schur est isomorphe à , où [A, B] est le sous-groupe engendré par les commutateurs aba−1b−1 pour a dans A et b dans B. Il peut aussi être exprimé en termes de cohomologie, comme . (fr)
foaf:depiction
dcterms:subject	Group theory Homological algebra
Wikipage page ID	1121587 (xsd:integer)
Wikipage revision ID	1070125719 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Presentation of a group Projective general linear group Projective representation Samuel Eilenberg Saunders Mac Lane Elementary abelian group Elementary matrix List of finite simple groups Baumslag–Solitar group Derived subgroup Algebraic K-theory Trivial group Periodic group Group theory Covering groups of the alternating and symmetric groups General linear group Natural transformation Normal subgroup Simple group Combinatorial group theory Perfect group Proceedings of the American Mathematical Society Subgroup Superperfect group Center (group theory) Central extension (mathematics) Topology Acyclic group Graduate Texts in Mathematics Quaternion group Group cohomology Group homology Heinz Hopf Todd–Coxeter algorithm Homological algebra Abelian group Advances in Mathematics Sylow subgroup Dihedral group Direct product of groups Bulletin of the AMS Free group Group representation Group theory Nonabelian group of order 6 Quasisimple group Universal covering space Springer-Verlag Center of a group Efficient group Journal für die reine und angewandte Mathematik Cohomology of groups Deficiency (group theory) Isoclinic Isoclinism
Link from a Wikipage to an external page	http://www-users.math.umd.edu/~jmr/KThy_errata2.pdf https://books.google.com/books%3Fid=TtMkTEZbYoYC http://projecteuclid.org/euclid.bams/1183551591%7Cdoi=10.1090/s0273-0979-1984-15273-x%7Cdoi-access=free http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN002165511 http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN00216633X
sameAs	Schur multiplier Schur multiplier Schur multiplier Schur multiplier Schur multiplier
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Citation dbt:Harv dbt:Refbegin dbt:Refend dbt:Reflist dbt:Harvs dbt:Eom dbt:Group_theory_sidebar
thumbnail	wiki-commons:Special:FilePath/Projective-representation-lifting.svg?width=300
authorlink	Issai Schur (en)
first	Issai (en) Leonid Viktorovich (en)
id	S/s083460 (en)
last	Kuzmin (en) Schur (en)
title	Schur multiplicator (en)
year	1904 (xsd:integer)

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