J Austral Math Soc Ser A 50 pp108--115, 1991.

Cup Products and Group Extensions

P. A. Linnell

(Received 30 June 1989; revised 19 December 1989)

Abstract

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.

1980 AMS Subject Classification (1985 Revision): primary 20J05; secondary 20E22

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Authors

P. A. Linnell: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0123, U.S.A.

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