Determining Hypercentral Hall Subgroups in Finite Groups

IF 1 3区数学 Q1 MATHEMATICS Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-08-12 DOI:10.1007/s40840-024-01752-x

V. Sotomayor

引用次数: 0

Abstract

Let G be a finite group, and let $\pi $ be a set of primes. The aim of this paper is to obtain some results concerning how much information about the $\pi $-structure of G can be gathered from the knowledge of the sizes of conjugacy classes of its $\pi $-elements and of their multiplicities. Among other results, we prove that this multiset of class sizes determines whether G has a hypercentral Hall $\pi $-subgroup.

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确定有限群中的超中心霍尔子群

让 G 是一个有限群，让 $\pi $是一组素数。本文的目的是得到一些结果，这些结果涉及从 G 的 $\pi$ 元素的共轭类的大小及其乘数的知识中可以收集到多少关于 G 的 $\pi$ 结构的信息。在其他结果中，我们证明了类大小的多集决定了 G 是否有一个超中心霍尔（\pi \）子群。

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

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.

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