强基两个群。

IF 0.8 Q2 MATHEMATICS

Vietnam Journal of Mathematics Pub Date : 2023-01-01 Epub Date: 2023-05-10 DOI:10.1007/s10013-023-00628-0

Timothy C Burness, Robert M Guralnick

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引用次数: 0

摘要

设G是有限群，设H是无核子群，设b（G，H）表示G对G/H作用的基大小。设α（G）为G的无核子群H与b（G，H）≥3的共轭类的个数。如果α（G）≤1，则G是强基二群，这意味着G的几乎每个忠实传递置换表示都有基大小2。本文研究了具有平凡Frattini子群的强基两个有限群。

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Strongly Base-Two Groups.

Let G be a finite group, let H be a core-free subgroup and let b(G, H) denote the base size for the action of G on G/H. Let $α (G)$ be the number of conjugacy classes of core-free subgroups H of G with $b (G, H) \geq 3$ . We say that G is a strongly base-two group if $α (G) \leq 1$ , which means that almost every faithful transitive permutation representation of G has base size 2. In this paper, we study the strongly base-two finite groups with trivial Frattini subgroup.

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来源期刊

Vietnam Journal of Mathematics MATHEMATICS-

CiteScore

1.90

自引率

0.00%

发文量

期刊介绍： Vietnam Journal of Mathematics was originally founded in 1973 by the Vietnam Academy of Science and Technology and the Vietnam Mathematical Society. Published by Springer from 1997 to 2005 and since 2013, this quarterly journal is open to contributions from researchers from all over the world, where all submitted articles are peer-reviewed by experts worldwide. It aims to publish high-quality original research papers and review articles in all active areas of pure and applied mathematics.