Cohomological detection and regular elements in group cohomology期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Cohomological detection and regular elements in group cohomology

Authors:	Jon F Carlson Hans-Werner Henn

Institution:	Department of Mathematics, University of Georgia, Athens, Georgia 30602 ; Mathematisches Institut der Universität, Im Neuenheimer Feld 288, D--69120 Heidelberg, Federal Republic of Germany

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 $\mathcal{O}$ is a set of elementary abelian -subgroups such that the cohomology is detected on the centralizers of the elements of $\mathcal{O}$ . Assume also that $\mathcal{O}$ is closed under conjugation and that is in $\mathcal{O}$ whenever some subgroup of is in $\mathcal{O}$ . Then there exists a regular element $\zeta$ in the cohomology ring such that the restriction of $\zeta$ to an elementary abelian -subgroup is not nilpotent if and only if is in $\mathcal{O}$ . 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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