Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-29T03:49:13.036Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Higgs, R. J., ‘Projective characters of degree one and the inflation-restriction sequence’, J. Austral. Math. Soc. Ser. A 46 (1989), 272–280.CrossRefGoogle Scholar
[2]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 134, Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[3]Isaacs, I. M., Character theory of finite groups (Pure and Applied Mathematics, a series of monographs and textbooks 69, Academic Press, New York, London, 1976).Google Scholar
[4]Karpilovsky, G., Projective representations of finite groups (Monographs and textbooks in pure and applied mathematics 94, Marcel Dekker, New York, Basel, 1985).Google Scholar
[5]Karpilovsky, G., The Schur multiplier (London Mathematical Society Monographs, (N.S.) 2, Oxford University Press, Oxford, New York, 1987).Google Scholar
[6]MacDonald, I. D., ‘Commutators and their products’, Amer. Math. Monthly 93 (1986), 440–443.CrossRefGoogle Scholar
[7]Mangold, Ruth, ‘Beitrage zur Theorie der Darstellungen endlicher Gruppen durch Kollineationen’, Mitt. Math. Sem. Giessen 69 (1966), (ii) 1–44.Google Scholar