The finite groups with three automorphism orbits

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-05-02 DOI:10.1016/j.jalgebra.2025.04.028

Cai Heng Li, Yan Zhou Zhu

引用次数: 0

Abstract

A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem initiated by G. Higman in 1963. As a consequence, a classification is obtained for finite permutation groups of rank 3 which are holomorphs of groups.

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具有三个自同构轨道的有限群

给出了元素被自同构群划分为三个轨道的有限群的完全分类，解决了1963年G. Higman提出的长期存在的分类问题。由此得到了群全纯的3阶有限置换群的一个分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.