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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exponents and the cohomology of finite groups


Author: Jonathan Pakianathan
Journal: Proc. Amer. Math. Soc. 128 (2000), 1893-1897
MSC (1991): Primary 20J06, 17B50; Secondary 17B56
Published electronically: November 1, 1999
MathSciNet review: 1646202
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05214-4
PII: S 0002-9939(99)05214-4
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
Article copyright: © Copyright 2000 American Mathematical Society