THE CLASSIFICATION OF 3/2-TRANSITIVE PERMUTATION GROUPS AND 1/2-TRANSITIVE LINEAR GROUPS

被引：9

作者：

Liebeck, Martin W. ^{[1
]}

Praeger, Cheryl E. ^{[2
]}

Saxl, Jan ^{[3
]}

机构：

[1] Imperial Coll, Dept Math, London SW7 2BZ, England

[2] Univ Western Australia, Sch Math & Stat, Perth, WA 6009, Australia

[3] Univ Cambridge, CMS, DPMMS, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 12期

基金：

澳大利亚研究理事会;

关键词：

D O I：

10.1090/proc/13243

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：5023 / 5037

页数：15

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