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Proceedings of the American Mathematical Society

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

 

 

Fixed-point-free actions on a class of abelian groups


Author: P. M. Curran
Journal: Proc. Amer. Math. Soc. 57 (1976), 189-193
MSC: Primary 20J05
DOI: https://doi.org/10.1090/S0002-9939-1976-0414739-1
MathSciNet review: 0414739
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Abstract: It is proved that all cohomology groups of a group $ G$ acting on an abelian group of a certain type vanish if the action of some subnormal abelian subgroup of $ G$ is fixed-point-free. This result is then applied to obtain results about group extensions and about the complete reducibility of linear groups.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0414739-1
Keywords: Group cohomology, group extensions, linear groups, complete reducibility, fixed-point-free actions
Article copyright: © Copyright 1976 American Mathematical Society