Extremely primitive groups and linear spaces

Melissa Lee, Gabriel Verret

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A finite non-regular primitive permutation group G is extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. Such groups have been studied for almost a century, finding various applications. The classification of extremely primitive groups was recently completed by Burness and Lee, who relied on an earlier classification of soluble extremely primitive groups by Mann, Praeger and Seress. Unfortunately, there is an inaccuracy in the latter classification. We correct this mistake, and also investigate regular linear spaces which admit groups of automorphisms that are extremely primitive on points.

Original languageEnglish
Pages (from-to)3227-3240
Number of pages14
JournalDesigns Codes and Cryptography
Volume91
Issue number10
DOIs
Publication statusPublished - Oct 2023

Keywords

  • Extremely primitive group
  • Line transitivity
  • Linear space
  • Point transitivity

Cite this