Covering the set of p-elements in finite groups by proper subgroups

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2024-09-20 DOI:10.1016/j.jcta.2024.105954

Attila Maróti , Juan Martínez , Alexander Moretó

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引用次数: 0

Abstract

Let p be a prime and let G be a finite group which is generated by the set $G_{p}$ of its p-elements. We show that if G is solvable and not a p-group, then the minimal number $σ_{p} (G)$ of proper subgroups of G whose union contains $G_{p}$ is equal to 1 less than the minimal number of proper subgroups of G whose union is G. For p-solvable groups G, we always have $σ_{p} (G) \geq p + 1$ . We study the case of alternating and symmetric groups G in detail.

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用适当的子群覆盖有限群中 p 元素的集合

设 p 是素数，G 是有限群，由其 p 元素集 Gp 生成。我们证明，如果 G 是可解而非 p 群，那么其联合包含 Gp 的 G 的适当子群的最小数目 σp(G) 等于比其联合是 G 的 G 的适当子群的最小数目少 1。对于 p 可解群 G，我们总是有 σp(G)≥p+1。我们将详细研究交替群和对称群 G 的情况。

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 Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.