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Proceedings of the American Mathematical Society

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On exponents of homology and cohomology of finite groups


Author: Jon F. Carlson
Journal: Proc. Amer. Math. Soc. 102 (1988), 814-816
MSC: Primary 20J06
DOI: https://doi.org/10.1090/S0002-9939-1988-0934848-6
MathSciNet review: 934848
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Abstract: Let $ G$ be a finite group and let $ r$ be the maximum of the $ p$-ranks of $ G$ for all primes $ p$ dividing the order to $ G$. There exist positive integers $ m$ and $ n$ such that the exponents of $ {H^n}(G,{\mathbf{Z}})$ and $ {H_m}(G,{\mathbf{Z}})$ are greater than $ \vert G{\vert^{1/r}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0934848-6
Keywords: Homology of finite groups, cohomology of finite groups
Article copyright: © Copyright 1988 American Mathematical Society