On cohomology rings of infinite groups

Eli Aljadeff

doi:10.1016/j.jpaa.2006.05.015

On cohomology rings of infinite groups

Eli Aljadeff^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let R be any ring (with 1), G a torsion free group and R G the corresponding group ring. Let Ext_{R 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 ∈ Ext_{R G}^* (M, M) is nilpotent (under Yoneda's product) if and only if its restriction to Ext_{R 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 language	English
Pages (from-to)	1099-1102
Number of pages	4
Journal	Journal of Pure and Applied Algebra
Volume	208
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2006.05.015
State	Published - Mar 2007
Externally published	Yes

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10.1016/j.jpaa.2006.05.015

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abstract = "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.",

author = "Eli Aljadeff",

year = "2007",

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doi = "10.1016/j.jpaa.2006.05.015",

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AU - Aljadeff, Eli

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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.

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VL - 208

SP - 1099

EP - 1102

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -

On cohomology rings of infinite groups

Abstract

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