{"title":"论有限群的循环作用","authors":"Lü Gong, Qilin Chen, Baojun Li","doi":"10.1007/s00009-024-02626-z","DOIUrl":null,"url":null,"abstract":"<p>Let <i>A</i> act on a group <i>G</i>. <i>A</i> is said to act <i>p</i>-cyclically on <i>G</i> if <span>\\(A^{{\\mathfrak {N}}_p {\\mathfrak {A}}_{p-1}}\\)</span> acts stably on <span>\\(G/O_{p'}(G)\\)</span>, and <i>A</i> is said to act cyclically on <i>G</i> if <i>A</i> acts <i>p</i>-cyclically on <i>G</i> for all primes <i>p</i>. In this paper, the actions of a group <i>A</i> on a <i>p</i>-group or <i>p</i>-soluble group <i>G</i> are investigated and some criteria of an action to be cyclic or <i>p</i>-cyclic are obtained.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Cyclic Actions of Finite Groups\",\"authors\":\"Lü Gong, Qilin Chen, Baojun Li\",\"doi\":\"10.1007/s00009-024-02626-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>A</i> act on a group <i>G</i>. <i>A</i> is said to act <i>p</i>-cyclically on <i>G</i> if <span>\\\\(A^{{\\\\mathfrak {N}}_p {\\\\mathfrak {A}}_{p-1}}\\\\)</span> acts stably on <span>\\\\(G/O_{p'}(G)\\\\)</span>, and <i>A</i> is said to act cyclically on <i>G</i> if <i>A</i> acts <i>p</i>-cyclically on <i>G</i> for all primes <i>p</i>. In this paper, the actions of a group <i>A</i> on a <i>p</i>-group or <i>p</i>-soluble group <i>G</i> are investigated and some criteria of an action to be cyclic or <i>p</i>-cyclic are obtained.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00009-024-02626-z\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00009-024-02626-z","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
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。
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.
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.