Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4597835 | Journal of Pure and Applied Algebra | 2007 | 4 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Eli Aljadeff,