A rigidity theorem for group extensions
type: Item
instance of: scholarly article
title: A rigidity theorem for group extensions
zbMATH Open document ID: 1003.20036
published in: Archiv der Mathematik
publication date: 2003-01-19T00:00:00Z
review text: Let \(S\) denote the class of fundamental groups of closed surfaces of genus \(g\geq 2\). Denote by \(S^n\) the class of groups \(G\) admitting a filtration \(G=G_n\supset G_{n+1}\supset\cdots\supset G_1\supset G_0=\{1\}\), \(G_i\triangleleft G_{i+1}\), such that \(G_{i+1}/G_i\) lies in \(S\). One says that \(G\) possesses a poly-\(S\) structure if \(G\in S^n\) for some \(n\). The author proves that any group \(G\) possesses a poly-\(S\) structure.
Mathematics Subject Classification ID: 20F22
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1346249
zbMATH Keywords: group extensions
zbMATH Keywords: fundamental groups
zbMATH Keywords: closed surfaces
author: F. E. A. Johnson
MaRDI profile type: Publication
full work available at URL: s000130050371
OpenAlex ID: W1999840070
DOI: 10.1007/S000130050371
description: scientific article; zbMATH DE number 1346249