Construction of finite p-groups with prescribed group of noncentral automorphisms
type: Item
instance of: scholarly article
title: Construction of finite p-groups with prescribed group of noncentral automorphisms
zbMATH Open document ID: 0607.20018
author: Panagiotis C. Soules
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108050
review text: Liebeck and the reviewer have used graphs for the construction of p- groups G of class two such that a given group K, acting as semiregular permutation group on the basis of G/G' is isomorphic to Aut G/Aut\({}_ c G\). The author shows that the graph can be chosen such that the action is regular if K is isomorphic to \(S_ n\) with \(n>4\), to \(A_ n\) with \(n>5\), to \(C_ 5 wr C_ 5\), and to PGL(2,p) or PSL(2,p) with \(p\geq 13\). For the latter cases a general statement on the existence of a suitable graph for groups \(K=<x,y>\) with conditions on certain product orders is needed (Lemma 5.1.1).
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 3981426
zbMATH Keywords: non-central automorphisms
zbMATH Keywords: graphs
zbMATH Keywords: p-groups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
cites work: Q3251484
cites work: Q5572939
cites work: The occurrence of finite groups in the automorphism group of nilpotent groups of class 2
cites work: A note on a theorem of Heineken and Liebeck
cites work: The occurrence of groups as automorphisms of nilpotent p-groups
cites work: Eine Bemerkung zu einer Arbeit von Heineken und Liebeck
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description: scientific article; zbMATH DE number 3981426