A vanishing theorem for cohomology

Alperin, J. L.; Gorenstein, Daniel

doi:10.1090/S0002-9939-1972-0291293-5

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A vanishing theorem for cohomology
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by J. L. Alperin and Daniel Gorenstein PDF

Proc. Amer. Math. Soc. 32 (1972), 87-88 Request permission

Abstract:

A criterion is given for ${H^0}(G,A) = {H^1}(G,A) = 0$, where G is a group and A is a G-module, in terms of the cohomology of a collection of subgroups of G.

References

Norman Blackburn, The extension theory of the symmetric and alternating groups, Math. Z. 117 (1970), 191–206. MR 286880, DOI 10.1007/BF01109843
D. G. Higman, Flag-transitive collineation groups of finite projective spaces, Illinois J. Math. 6 (1962), 434–446. MR 143098