Cohomological detection and regular elements in group cohomology

Authors:
Jon F. Carlson and Hans-Werner Henn

Journal:
Proc. Amer. Math. Soc. **124** (1996), 665-670

MSC (1991):
Primary 20J05, 20J06, 55R40

DOI:
https://doi.org/10.1090/S0002-9939-96-03331-X

MathSciNet review:
1327000

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Abstract: Suppose that is a compact Lie group or a discrete group of finite virtual cohomological dimension and that is a field of characteristic . Suppose that is a set of elementary abelian -subgroups such that the cohomology is detected on the centralizers of the elements of . Assume also that is closed under conjugation and that is in whenever some subgroup of is in . Then there exists a regular element in the cohomology ring such that the restriction of to an elementary abelian -subgroup is not nilpotent if and only if is in . The converse of the result is a theorem of Lannes, Schwartz and the second author. The results have several implications for the depth and associated primes of the cohomology rings.

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Additional Information

**Jon F. Carlson**

Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602

Email:
jfc@sloth.math.uga.ed

**Hans-Werner Henn**

Affiliation:
Mathematisches Institut der Universität, Im Neuenheimer Feld 288, D–69120 Heidelberg, Federal Republic of Germany

Email:
henn@mathi.uni-heidelberg.de

DOI:
https://doi.org/10.1090/S0002-9939-96-03331-X

Received by editor(s):
December 22, 1993

Additional Notes:
The first author was partially supported by a grant from NSF.

The second author was supported by a Heisenberg grant from DFG.

Communicated by:
Eric Friedlander

Article copyright:
© Copyright 1996
American Mathematical Society