Article ID Journal Published Year Pages File Type
4597835 Journal of Pure and Applied Algebra 2007 4 Pages PDF
Abstract

Let RR be any ring (with 1), GG a torsion free group and RGRG the corresponding group ring. Let ExtRG∗(M,M) be the cohomology ring associated with the RGRG-module MM. Let HH be a subgroup of finite index of GG. The following is a special version of our main Theorem: Assume the profinite completion of GG is torsion free. Then an element ζ∈ExtRG∗(M,M) is nilpotent (under Yoneda’s product) if and only if its restriction to ExtRH∗(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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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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