J Austral Math Soc Ser A 48 pp497--505, 1990.

Subgroups of the Schur Multiplier

R. J. Higgs

Abstract

Two subgroups M_E(G) and M₁(G) of the Schur multiplier M(G) of a finite group G are introduced: M_E(G) contains those cohomology classes [a] of M(G) for which every element of G is a-regular, and M₁(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 M₁(G) can be expressed as the product of an element of M_E(G) and an element of the image of the inflation homomorphism from M(G/G¢) into M(G).

1980 AMS Subject Classification (1985 Revision): 20C25

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Authors

R. J. Higgs

University College Dublin, Belfield, Dublin 4, Ireland.