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 | 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]**Alejandro Adem,*Cohomological exponents of 𝑍𝐺-lattices*, J. Pure Appl. Algebra**58**(1989), no. 1, 1–5. MR**996170**, 10.1016/0022-4049(89)90048-0**[BrP]**W. Browder, J. Pakianathan,*Cohomology of uniformly powerful -groups,*preprint.**[B]**Kenneth S. Brown,*Cohomology of groups*, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1994. Corrected reprint of the 1982 original. MR**1324339****[C]**G. Carlsson, R. L. Cohen, H. R. Miller, and D. C. Ravenel (eds.),*Algebraic topology*, Lecture Notes in Mathematics, vol. 1370, Springer-Verlag, Berlin, 1989. MR**1000361****[Le]**I. J. Leary,*A bound on the exponent of the cohomology of 𝐵𝐶-bundles*, Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guíxols, 1994) Progr. Math., vol. 136, Birkhäuser, Basel, 1996, pp. 255–259. MR**1397736**

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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

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