 
Summary: Journal of Pure and Applied Algebra 208 (2007) 10991102
www.elsevier.com/locate/jpaa
On cohomology rings of infinite groups
Eli Aljadeff
Department of Mathematics, Technion Israel Institute of Technology, 32000 Haifa, Israel
Received 17 October 2005; received in revised form 24 March 2006
Available online 2 August 2006
Communicated by C. Kassel
Abstract
Let R be any ring (with 1), G a torsion free group and RG the corresponding group ring. Let Ext
RG(M, M) be the cohomology
ring associated with the RGmodule M. Let H be a subgroup of finite index of G. The following is a special version of our main
Theorem: Assume the profinite completion of G is torsion free. Then an element Ext
RG(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.
c 2006 Elsevier B.V. All rights reserved.
MSC: 20J06; 20E18; 16S35
1. Introduction
