Groups with no infinite perfect subgroups and aspherical 2-complexes
type: Item
instance of: scholarly article
title: Groups with no infinite perfect subgroups and aspherical 2-complexes
zbMATH Open document ID: 0791.57003
DOI: 10.1007/BF02565823
author: M. Dyer
published in: Commentarii Mathematici Helvetici
publication date: 1994-07-19T00:00:00Z
full work available at URL: https://eudml.org/doc/140306
review text: This paper is a further contribution of the author to J. H. C. Whitehead's question whether every subcomplex of an aspherical 2-complex is also aspherical. The main result is that, if \(P\) is a nontrivial, finite, superperfect, normal subgroup of a finitely presented group \(G\) such that \(Q = G/P\) has cohomological dimension 1 or 2, then \(G\) is not \(P\)-Cockroft. As a consequence, Whitehead's question is answered positively, if the fundamental group of the subcomplex has no infinite perfect subgroups. This improves a result of J. F. Adams.
Mathematics Subject Classification ID: 57M20
zbMATH DE Number: 484352
zbMATH Keywords: subcomplex of an aspherical 2-complex
zbMATH Keywords: nontrivial, finite, superperfect, normal subgroup of a finitely presented group
zbMATH Keywords: cohomological dimension
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 484352