{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219498825502032","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
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.
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