On cohomology rings of infinite groups

2005/02/24 by Eli Aljadeff, Aljadeff, Eli
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #math.GR #math.KT

paper · pdf · doi:10.48550/arxiv.math/0502513

6 pages

arxiv created 2008/12/17 · arxiv updated 2009/12/01

Abstract

Let R be any ring (with 1), Γa group and RΓthe corresponding group ring. Let Ext_RΓ^*(M,M) be the cohomology ring associated to the RΓ-module M. Let H be a subgroup of finite index of Γ. The following is a special version of our main Theorem: Assume the profinite completion of Γis torsion free. Then an element ζin Ext_RΓ^*(M,M) is nilpotent (under Yoneda's product) if and only if its restriction to Ext_RH^*(M,M) is nilpotent. In particular this holds for the Thompson group. There are torsion free groups for which the analogous statement is false.

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