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Subgroups of the Schur multiplier

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

R. J. Higgs
R. J. Higgs
Affiliation:
University College DublinBelfield Dublin 4, Ireland
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Abstract

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Two subgroups ME(G) and MI(G) of the Schur multiplier M(G) of a finite group G are introduced: ME(G) contains those cohomology classes [α] of M(G) for which every element of G is α-regular, and MI(G) consists of those cohomology classes of M(G) which contain a G-invariant cocycle. It is then shown that under suitable circumstances, such as when G has odd order, that each element of MI(G) can be expressed as the product of an element of ME(G) and an element of the image of the inflation homomorphism from M(G/G′) into M(G).

Keywords

Schur multiplier.

MSC classification

Secondary: 20C25: Projective representations and multipliers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 497 - 505
Copyright
Copyright © Australian Mathematical Society 1990

References

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