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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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Exponents and the cohomology of finite groups
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by Jonathan Pakianathan PDF
Proc. Amer. Math. Soc. 128 (2000), 1893-1897 Request permission

Abstract:

We will provide an example of a $p$-group $G$ which has elements of order $p^3$ in some of its integral cohomology groups but which also has the property that $p^2$ annihilates $\bar {H}^i(G;\mathbb {Z})$ for all sufficiently high $i$. This provides a counterexample to a conjecture of A. Adem which states that if a finite group $K$ has an element of order $p^n$ in one of its integral cohomology groups, then it has such an element in infinitely many of its cohomology groups.
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Additional Information
  • Jonathan Pakianathan
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: pakianat@math.wisc.edu
  • Received by editor(s): March 16, 1998
  • Received by editor(s) in revised form: August 13, 1998
  • Published electronically: November 1, 1999
  • Communicated by: Ralph Cohen
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 1893-1897
  • MSC (1991): Primary 20J06, 17B50; Secondary 17B56
  • DOI: https://doi.org/10.1090/S0002-9939-99-05214-4
  • MathSciNet review: 1646202