A family of quasiprimitive 2-arc transitive graphs which have non-quasiprimitive full automorphism groups
type: Item
instance of: scholarly article
title: A family of quasiprimitive 2-arc transitive graphs which have non-quasiprimitive full automorphism groups
zbMATH Open document ID: 0913.05052
author: Cai Heng Li
published in: European Journal of Combinatorics
publication date: 1999-06-08T00:00:00Z
review text: A group \(G\) is said to act quasiprimitively on a graph \(\Gamma\) if every nontrivial normal subgroup of \(G\) acts transitively on the vertex set of \(\Gamma\). The action of \(G\) on \(\Gamma\) is 2-arc transitive if \(G\) acts transitively on the set of 2-arcs, that is on the set of ordered triples \((x,y,z)\) of vertices of \(\Gamma\) such that \(x\) and \(z\) are distinct vertices adjacent to \(y\). For each prime \(p\equiv 1\) or \(-1\pmod {24}\) a graph \(\Gamma\) is constructed on which \(G\cong \text{PSL}_2 (p)\) acts quasiprimitively and 2-arc transitively, such that the full automorphism group \(\Aut\Gamma\) of \(\Gamma\) is isomorphic to \(\text{PSL}_2 (p)\times \mathbb{Z}_2\) and the action of \(\Aut\Gamma\) is not quasiprimitive.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1199930
zbMATH Keywords: quasiprimitive
zbMATH Keywords: automorphism group
reviewed by: Alexander A. Ivanov
MaRDI profile type: Publication
full work available at URL: eujc.1997.0194
OpenAlex ID: W2113966410
DOI: 10.1006/EUJC.1997.0194
description: scientific article; zbMATH DE number 1199930