Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
group theory concept
|
| gptkbp:alsoKnownAs |
second homology group of a group
|
| gptkbp:application |
central extensions of groups
classification of projective representations |
| gptkbp:citation |
gptkb:Schur,_I._(1904)._"Über_die_Darstellung_der_endlichen_Gruppen_durch_gebrochene_lineare_Substitutionen"
|
| gptkbp:defines |
the second homology group H_2(G, Z) for a group G
the second cohomology group H^2(G, C^*) for a group G |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasSubfield |
group theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schur multiplier
|
| gptkbp:introducedIn |
1904
|
| gptkbp:namedAfter |
gptkb:Issai_Schur
|
| gptkbp:notation |
H_2(G, Z)
M(G) |
| gptkbp:property |
is a functor from groups to abelian groups
is finite for finite groups is trivial for free groups measures the obstruction to a projective representation being linear |
| gptkbp:relatedTo |
representation theory
group cohomology group extensions |
| gptkbp:bfsParent |
gptkb:Group_theory
|
| gptkbp:bfsLayer |
5
|