Characterisations of \(A_{p+2}\) and \(L_ 2(2^ q)\)
type: Item
instance of: scholarly article
title: Characterisations of \(A_{p+2}\) and \(L_ 2(2^ q)\)
zbMATH Open document ID: 0877.20002
author: Mong Lung Lang
published in: Archiv der Mathematik
publication date: 1997-07-06T00:00:00Z
review text: Finite transitive permutation groups of degree \(p+2\) are considered which contain a cycle of prime length \(p\geq 5\). (Clearly, such a group is triply-transitive, and it is easily shown that the unique minimal normal subgroup \(N\) of \(G\) is also triply-transitive.) Based on the fact that a simple triply-transitive group of degree \(p+2\) is either permutation isomorphic to the alternating group \(A_{p+2}\) or to \(L_2(2^q)\) in its natural representation of degree \(2^q+1\) where \(p=2^q-1\), all these groups are classified. -- The fact mentioned is not proved in the paper, but it follows from the classification of finite simple groups.
Mathematics Subject Classification ID: 20B10
Mathematics Subject Classification ID: 20B20
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 1028208
zbMATH Keywords: triply-transitive permutation groups
zbMATH Keywords: prime order cycles
zbMATH Keywords: alternating groups
zbMATH Keywords: linear fractional groups
zbMATH Keywords: finite transitive permutation groups
zbMATH Keywords: minimal normal subgroups
MaRDI profile type: Publication
full work available at URL: s000130050069
OpenAlex ID: W2057776309
cites work: Q5848209
cites work: Finite permutation groups of rank 3
DOI: 10.1007/S000130050069
description: scientific article; zbMATH DE number 1028208