The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups

Martin W. Liebeck, Cheryl E. Praeger, Jan Saxl

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
199 Downloads (Pure)

Abstract

A linear group G ≤ GL(V ), where V is a finite vector space, is called 1 2 -transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the 1 2 -transitive linear groups. As a consequence we complete the determination of the finite 3 2 -transitive permutation groups - the transitive groups for which a point-stabilizer has all its nontrivial orbits of the same size. We also determine the (k + 1 2 )-transitive groups for integers k ≥ 2.

Original languageEnglish
Pages (from-to)5023-5037
Number of pages15
JournalProceedings of the American Mathematical Society
Volume147
Issue number12
DOIs
Publication statusPublished - 1 Jan 2019

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