TY - JOUR

T1 - On cohomology rings of infinite groups

AU - Aljadeff, Eli

N1 - Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33751340078&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2006.05.015

DO - 10.1016/j.jpaa.2006.05.015

M3 - 文章

AN - SCOPUS:33751340078

VL - 208

SP - 1099

EP - 1102

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

ER -