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

DOI:
https://doi.org/10.1090/S0002-9939-99-05214-4

Published electronically:
November 1, 1999

MathSciNet review:
1646202

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Abstract | References | Similar Articles | Additional Information

Abstract: We will provide an example of a -group which has elements of order in some of its integral cohomology groups but which also has the property that annihilates for all sufficiently high . This provides a counterexample to a conjecture of A. Adem which states that if a finite group has an element of order in one of its integral cohomology groups, then it has such an element in infinitely many of its cohomology groups.

**[A]**A. Adem,*Cohomological exponents of -lattices,*J. Pure and Appl. Alg.**58**(1989). MR**90b:20046****[BrP]**W. Browder, J. Pakianathan,*Cohomology of uniformly powerful -groups,*preprint.**[B]**K. S. Brown,*Cohomology of Groups*, Springer Verlag GTM 87, New York-Heidelberg-Berlin, 1994. MR**96a:20072****[C]**G. Carlsson, R. L. Cohen, H. R. Miller, D. C. Ravenel,*Algebraic Topology,*Springer Verlag Lecture Notes in Mathematics 1370, New York-Heidelberg-Berlin, 1989. MR**90a:55003****[Le]**I. J. Leary,*A bound on the exponent of the cohomology of -bundles,*Proceedings of the 1994 Barcelona Conference on Algebraic Topology: Progress in Mathematics, Vol.**136**(1996) pp. 255-260, Birkhauser-Verlag. MR**97k:55018**

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Additional Information

**Jonathan Pakianathan**

Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Email:
pakianat@math.wisc.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05214-4

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