Representing the sporadic groups as noncentral automorphisms of \(p\)-groups
type: Item
instance of: scholarly article
title: Representing the sporadic groups as noncentral automorphisms of \(p\)-groups
zbMATH Open document ID: 0858.20024
author: Panagiotis C. Soules
author: Andrew J. Woldar
published in: Journal of Algebra
publication date: 1997-03-18T00:00:00Z
review text: By a result of Liebeck and the reviewer there is, for every finite group \(G\), a \(p\)-group \(L\) of class 2 such that \(G\) is isomorphic to \(\text{Aut}(L)/\text{Aut}_c(L)\) where \(\text{Aut}_c(L)\) is the group of central automorphisms. In the original construction \(L/L'\) becomes a free \(G\)-module, freely generated by \(k\) elements where \(k\) depends on the order and the number of the generators of \(G\). The authors show, that for the sporadic groups a modification is possible such that \(k=1\). This requires a special choice of generators for the groups \(G\) considered.
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 941235
zbMATH Keywords: \(p\)-groups
zbMATH Keywords: noncentral automorphisms
zbMATH Keywords: group of central automorphisms
zbMATH Keywords: sporadic groups
zbMATH Keywords: generators
reviewed by: Hermann Heineken
MaRDI profile type: Publication
full work available at URL: jabr.1996.0324
OpenAlex ID: W2024491935
DOI: 10.1006/JABR.1996.0324
description: scientific article; zbMATH DE number 941235