Complexity and varieties for infinite groups. II
type: Item
instance of: scholarly article
title: Complexity and varieties for infinite groups. II
zbMATH Open document ID: 0886.20003
published in: Journal of Algebra
publication date: 1998-03-05T00:00:00Z
review text: [For part I see the preceding review Zbl 0886.20002.] The author studies the properties of the categories \(\text{Mod}(kG)\), \(\text{mod}(kG)\), \(\text{StMod}(kG)\), \(\text{stmod}(kG)\) for an \(LH{\mathfrak F}\)-group \(G\) and varieties of such modules. As application of these results he obtains the following important result. Theorem 19.1. Let \(G\) be an \(LH{\mathfrak F}\)-group of type \(FP_\infty\). Then there are only finitely many conjugacy classes in \(G\) of finite elementary abelian subgroups. The author notes that it is possible to obtain this theorem from results of Henn (unpublished) and Kropholler and Mislin.
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 1051522
zbMATH Keywords: categories of modules
zbMATH Keywords: varieties of modules
zbMATH Keywords: modules over group rings
zbMATH Keywords: restrictions
zbMATH Keywords: finite subgroups
author: David Benson
reviewed by: L. A. Kurdachenko
MaRDI profile type: Publication
full work available at URL: jabr.1996.6997
OpenAlex ID: W4210546622
cites work: Representations, resolutions and Quillen's dimension theorem
cites work: Etale homotopy
cites work: Q3997902
cites work: Complexity and varieties for infinite groups. I
cites work: Complexity and varieties for infinitely generated modules
cites work: Complexity and varieties for infinitely generated modules, II
cites work: Varieties for modules and a problem of Steenrod
cites work: The variety of an indecomposable module is connected
cites work: Projectivity and relative projectivity over group rings
cites work: Q4001605
cites work: Note on extensions of Abelian groups by primary groups
cites work: The spectrum of an equivariant cohomology ring. I. II
cites work: Homotopical algebra
cites work: Rational homotopy theory
cites work: Idempotent Modules in the Stable Category
DOI: 10.1006/JABR.1996.6997
description: scientific article; zbMATH DE number 1051522