On Cyclic Actions of Finite Groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-28 DOI:10.1007/s00009-024-02626-z

Lü Gong, Qilin Chen, Baojun Li

引用次数: 0

Abstract

Let A act on a group G. A is said to act p-cyclically on G if \(A^{{\mathfrak {N}}_p {\mathfrak {A}}_{p-1}}\) acts stably on \(G/O_{p'}(G)\), and A is said to act cyclically on G if A acts p-cyclically on G for all primes p. In this paper, the actions of a group A on a p-group or p-soluble group G are investigated and some criteria of an action to be cyclic or p-cyclic are obtained.

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论有限群的循环作用

如果 \(A^{{\mathfrak {N}}_p {math\frak {A}}_{p-1}}\) 稳定地作用于 \(G/O_{p'}(G)\)，则称 A 以 p 循环的方式作用于 G；如果对于所有素数 p，A 以 p 循环的方式作用于 G，则称 A 以循环的方式作用于 G。本文研究了群 A 在 p 群或 p 可溶群 G 上的作用，并得到了作用为循环或 p 循环的一些标准。

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.