Permutation complexes for profinite groups

Peter Symonds

doi:10.4171/CMH/83

Permutation complexes for profinite groups

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

Abstract

An important tool in the analysis of discrete groups of finite virtual cohomological dimension is the existence of a finite dimensional contractible CW-complex on which the group acts with finite stabilizers. We develop a purely algebraic analogue for profinite groups. This enables us to reveal the connection between finiteness conditions on the cohomology of the group and those on the normalizers of the finite p-subgroups. © Swiss Mathematical Society.

Original language	English
Pages (from-to)	1-37
Number of pages	36
Journal	Commentarii Mathematici Helvetici
Volume	82
Issue number	1
DOIs	https://doi.org/10.4171/CMH/83
Publication status	Published - 2007

Keywords

Cohomology
Permutation module
Profinite group

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10.4171/CMH/83

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title = "Permutation complexes for profinite groups",

abstract = "An important tool in the analysis of discrete groups of finite virtual cohomological dimension is the existence of a finite dimensional contractible CW-complex on which the group acts with finite stabilizers. We develop a purely algebraic analogue for profinite groups. This enables us to reveal the connection between finiteness conditions on the cohomology of the group and those on the normalizers of the finite p-subgroups. {\textcopyright} Swiss Mathematical Society.",

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AB - An important tool in the analysis of discrete groups of finite virtual cohomological dimension is the existence of a finite dimensional contractible CW-complex on which the group acts with finite stabilizers. We develop a purely algebraic analogue for profinite groups. This enables us to reveal the connection between finiteness conditions on the cohomology of the group and those on the normalizers of the finite p-subgroups. © Swiss Mathematical Society.

KW - Cohomology

KW - Permutation module

KW - Profinite group

U2 - 10.4171/CMH/83

DO - 10.4171/CMH/83

M3 - Article

SN - 0010-2571

VL - 82

SP - 1

EP - 37

JO - Commentarii Mathematici Helvetici

JF - Commentarii Mathematici Helvetici

IS - 1

ER -

Permutation complexes for profinite groups

Abstract

Keywords

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