On One Open Question of the Theory of $$\sigma $$ -Properties of a Finite Group

IF 1.1 4区数学 Q1 MATHEMATICS

Communications in Mathematics and Statistics Pub Date : 2024-07-05 DOI:10.1007/s40304-023-00390-2

A.-Ming Liu, Zhigang Wang, Vasily G. Safonov, Alexander N. Skiba

引用次数: 0

Abstract

Let $\sigma =\{\sigma _{i} \mid i\in I\}$ be some partition of the set of all primes and G a finite group. A subgroup A of G is $\sigma $-permutable in G provided G is $\sigma $-full; that is, G has a Hall $\sigma _{i}$-subgroup for all $i\in I$ and A permutes with all such Hall subgroups H of G; that is, $AH=HA$. Answering the Question 6.4 in Skiba (Probl Phys Math Tech 42(21):89–96, 2014), we get a description of finite $\sigma $-full groups G in which $\sigma $-permutability is a transitive relation.

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论有限群的 $$sigma $$ 特性理论的一个未决问题

让 \sigma =\{\sigma _{i} \mid i\in I\}\) 是所有素数集合的某个分区，而 G 是一个有限群。只要 G 是 $\sigma $-满的，那么 G 的一个子群 A 在 G 中是 $\sigma $-可变的；也就是说，G 对所有的 $i\in I$ 都有一个霍尔 $\sigma _{i}$-子群，并且 A 与 G 的所有这样的霍尔子群 H 都是包络的；也就是说， $AH=HA$。回答斯基巴（Probl Phys Math Tech 42(21):89-96，2014）中的问题 6.4，我们得到了有限$\sigma $-满群 G 的描述，其中$\sigma $-可变性是一个传递关系。

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

Communications in Mathematics and Statistics Mathematics-Statistics and Probability

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： Communications in Mathematics and Statistics is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences, University of Science and Technology of China (USTC). The journal will be committed to publish high level original peer reviewed research papers in various areas of mathematical sciences, including pure mathematics, applied mathematics, computational mathematics, and probability and statistics. Typically one volume is published each year, and each volume consists of four issues.