{"title":"论有限群中的下中心数列的规范","authors":"Lü Gong, Ziru Jing, Libo Zhao, Baojun Li","doi":"10.1142/s0219498825502032","DOIUrl":null,"url":null,"abstract":"<p>In this paper, the norm <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span> of the lower central series in a finite group <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> is introduced, which unifies the norm of derived subgroups and nilpotent residuals. Some propositions of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>G</mi><mo stretchy=\"false\">)</mo></math></span><span></span> are obtained, and some related subgroups as well as their equivalent propositions can also be found.</p>","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"145 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the norm of the lower central series in a finite group\",\"authors\":\"Lü Gong, Ziru Jing, Libo Zhao, Baojun Li\",\"doi\":\"10.1142/s0219498825502032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, the norm <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\\\"false\\\">(</mo><mi>G</mi><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> of the lower central series in a finite group <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>G</mi></math></span><span></span> is introduced, which unifies the norm of derived subgroups and nilpotent residuals. Some propositions of <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy=\\\"false\\\">(</mo><mi>G</mi><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> are obtained, and some related subgroups as well as their equivalent propositions can also be found.</p>\",\"PeriodicalId\":54888,\"journal\":{\"name\":\"Journal of Algebra and Its Applications\",\"volume\":\"145 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra and Its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219498825502032\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219498825502032","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了有限群 G 中下中心数列的规范 Li(G)，它统一了导出子群和无穷残差的规范。本文得到了 Li(G) 的一些命题，还找到了一些相关子群及其等价命题。
On the norm of the lower central series in a finite group
In this paper, the norm of the lower central series in a finite group is introduced, which unifies the norm of derived subgroups and nilpotent residuals. Some propositions of are obtained, and some related subgroups as well as their equivalent propositions can also be found.
期刊介绍：
The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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