Linear groups and distance-transitive graphs
type: Item
instance of: scholarly article
title: Linear groups and distance-transitive graphs
zbMATH Open document ID: 0683.05023
DOI: 10.1016/S0195-6698(89)80013-7
author: John van Bon
author: Arjeh M. Cohen
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: The main theorem of this paper reads as follows: Let G be a group with \(PSL(n,q)\trianglelefteq G\leq aut PSL(n,q),\) \(n\geq 2\) and (n,q)\(\neq (2,2)\), (2,3). If \(\Gamma\) is a connected graph of diameter at least 2 on which G acts primitively and distance-transitively, then either \(\Gamma\) is a Grassmann graph or \(K:=N_{aut \Gamma}(G^{\infty})\), \(\Gamma\) and the stabilizer H in K of a vertex are as listed in a Table (16 cases).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 4118395
zbMATH Keywords: linear group
zbMATH Keywords: transitive action
reviewed by: Ulrich Knauer
MaRDI profile type: Publication
cites work: On finite groups generated by odd transpositions. IV
cites work: On the maximal subgroups of the finite classical groups
cites work: Q3218140
cites work: Q3977425
cites work: Q3992965
cites work: Q3684278
cites work: A note on decomposition numbers for general linear groups and symmetric groups
cites work: Finite groups generated by 3-transpositions. I
cites work: Two multiplicity-free permutation representations of the general linear group \(GL(n,q^ 2)\)
cites work: Locally petersen graphs
cites work: Distance-regular graphs and halved graphs
cites work: Multiplicity-free permutation representations of finite linear groups
cites work: Distance-transitive representations of the symmetric groups
cites work: Q3834071
cites work: The modular characters of the Mathieu groups
cites work: The Rank 3 Permutation Representations of the Finite Classical Groups
cites work: On the minimal degrees of projective representations of the finite Chevalley groups
cites work: On the Orders of Maximal Subgroups of the Finite Classical Groups
cites work: The Affine Permutation Groups of Rank Three
cites work: Distance transitive graphs with symmetric or alternating automorphism group
cites work: Q3926778
cites work: Distance-regular graphs with girth 3 or 4: I
full work available at URL: s0195-6698(89)80013-7
OpenAlex ID: W2142437685
description: scientific article; zbMATH DE number 4118395