On cohomology rings of infinite groups

Eli Aljadeff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let R be any ring (with 1), G a torsion free group and R G the corresponding group ring. Let ExtR G* (M, M) be the cohomology ring associated with the R G-module 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 ζ ∈ ExtR G* (M, M) is nilpotent (under Yoneda's product) if and only if its restriction to ExtR H* (M, M) is nilpotent. In particular this holds for the Thompson group. There are torsion free groups for which the analogous statement is false.

Original languageEnglish
Pages (from-to)1099-1102
Number of pages4
JournalJournal of Pure and Applied Algebra
Issue number3
StatePublished - Mar 2007
Externally publishedYes


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