The Higman-McLaughlin theorem for flag-transitive linear spaces
type: Item
instance of: scholarly article
title: The Higman-McLaughlin theorem for flag-transitive linear spaces
zbMATH Open document ID: 0712.20002
DOI: 10.1007/BF00150786
author: Francis Buekenhout
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: A well known theorem by Higman and McLaughlin states that, if a group G acts flag-transitively on a finite linear space S, then G also acts point-primitively on S. The author proves the following generalization of that theorem. Given S and G as above, let \(G^ 0\) be a normal subgroup of G of index at most 3 (and assume S has at least two lines, to avoid degenerate situations). Then \(G^ 0\) is still point-primitive on S, apart from three exceptions when \([G:G^ 0]=3\) and \(S=AG(2,2)\), AG(3,4) or AG(2,8). The proof is an elegant example of interaction between geometric and group-theoretic methods and is readable for a non professional group theorist too (like the reviewer, for instance).
Mathematics Subject Classification ID: 20B15
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 51A10
zbMATH DE Number: 4171196
zbMATH Keywords: primitive groups
zbMATH Keywords: finite linear space
zbMATH Keywords: point-primitive
reviewed by: Antonio Pasini
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00150786
OpenAlex ID: W2041058075
description: scientific article; zbMATH DE number 4171196