### 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 language | English |
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Title of host publication | Proceedings of the American Mathematical Society |

Pages | 5023-5037 |

Number of pages | 15 |

Volume | 147 |

Edition | 12 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

### Publication series

Name | Proceedings of the American Mathematical Society |
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Publisher | American Mathematical Society |

ISSN (Print) | 0002-9939 |

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### Cite this

*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

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*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.

Research output: Chapter in Book/Conference paper › Conference paper

TY - GEN

T1 - The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups

AU - Liebeck, Martin W.

AU - Praeger, Cheryl E.

AU - Saxl, Jan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074399402&partnerID=8YFLogxK

U2 - 10.1090/proc/13243

DO - 10.1090/proc/13243

M3 - Conference paper

VL - 147

T3 - Proceedings of the American Mathematical Society

SP - 5023

EP - 5037

BT - Proceedings of the American Mathematical Society

ER -