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Cup products and group extensions

Part of: Connections with homological algebra and category theory Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

P. A. Linnell
P. A. Linnell
Affiliation:
Department of Mathematics Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0123. U.S.A.E-mail address: LINNELL@VTMATH.BITNET
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Abstract

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Let G be a finitely generated group and let R be a commutative ring, regarded as a G-module with G acting trivially. We shall determine when the cup product of two elements of H1(G, R) is zero. Our method will use the interpretation of H2(G, R) as extensions of G by R. This will give an alternative demonstration of results of Hillman and Würfel.

Keywords

cup productgroup extension

MSC classification

Secondary: 20J05: Homological methods in group theory 20E22: Extensions, wreath products, and other compositions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 108 - 115
Copyright
Copyright © Australian Mathematical Society 1991

References

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