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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.