On the CSS-subgroups and the supersolvabilty of a finite group

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-11 DOI:10.1007/s11587-023-00839-0

Xianhe Zhao, Yuxin Zhao, Ruifang Chen, Xiuyun Guo

引用次数: 0

Abstract

Recall that a subgroup H of a finite group G is said to be a CSS-subgroup of G if there is a normal subgroup T of G such that \(G=HT\), and \(H\cap T\) is SS-quasinormal in G. Clearly, both the c-normal subgroups and the SS-quasinormal subgroups are the CSS-subgroups, but the converse does not hold. In this paper, based on the research of c-normality and SS-quainormality, with the help of the group formation theory, we investigate the supersolvabilty of G by assuming that the subgroups with order |D| are CSS-subgroups of G, where |D| is a prime power. Some relevant results to the c-normality and the SS-quainormality are generalized.

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论有限群的 CSS 子群和超可溶性

回想一下，如果有限群 G 的一个子群 H 存在一个正则子群 T，使得 \(G=HT\)，并且 \(H\cap T\) 在 G 中是 SS-准正则的，则称该子群 H 是 G 的 CSS 子群。显然，c-正则子群和 SS-准正则子群都是 CSS 子群，但反之不成立。本文在研究 c 正态性和 SS 正态性的基础上，借助群形成理论，假设阶为 |D| 的子群是 G 的 CSS 子群，其中 |D| 是素幂，从而研究 G 的超可溶性。一些与 c 正态性和 SS 正态性相关的结果得到了推广。

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.