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

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

Research output: Chapter in Book/Conference paperConference paper

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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
Title of host publicationProceedings of the American Mathematical Society
Pages5023-5037
Number of pages15
Volume147
Edition12
DOIs
Publication statusPublished - 1 Jan 2019

Publication series

NameProceedings of the American Mathematical Society
PublisherAmerican Mathematical Society
ISSN (Print)0002-9939

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Linear Group
Permutation group
Orbits
Vector spaces
Orbit
Vector space
Integer

Cite this

Liebeck, M. W., Praeger, C. E., & Saxl, J. (2019). The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups. In Proceedings of the American Mathematical Society (12 ed., Vol. 147, pp. 5023-5037). (Proceedings of the American Mathematical Society). https://doi.org/10.1090/proc/13243
Liebeck, Martin W. ; Praeger, Cheryl E. ; Saxl, Jan. / The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups. Proceedings of the American Mathematical Society. Vol. 147 12. ed. 2019. pp. 5023-5037 (Proceedings of the American Mathematical Society).
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Liebeck, MW, Praeger, CE & Saxl, J 2019, The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups. in Proceedings of the American Mathematical Society. 12 edn, vol. 147, Proceedings of the American Mathematical Society, pp. 5023-5037. https://doi.org/10.1090/proc/13243

The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups. / Liebeck, Martin W.; Praeger, Cheryl E.; Saxl, Jan.

Proceedings of the American Mathematical Society. Vol. 147 12. ed. 2019. p. 5023-5037 (Proceedings of the American Mathematical Society).

Research output: Chapter in Book/Conference paperConference paper

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Liebeck MW, Praeger CE, Saxl J. The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups. In Proceedings of the American Mathematical Society. 12 ed. Vol. 147. 2019. p. 5023-5037. (Proceedings of the American Mathematical Society). https://doi.org/10.1090/proc/13243