{"title":"A Jordan–Hölder type theorem for finite groups","authors":"Francesca Lisi","doi":"10.1007/s10231-024-01456-w","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the notion of <span>\\(\\mathbb {P}\\)</span>-subnormal subgroup in a finite group, which generalizes the one of subnormal subgroup. We prove an analogous of the well-known Jordan–Hölder Theorem for these subgroups and their related chains of subgroups.\n</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 6","pages":"2577 - 2590"},"PeriodicalIF":1.0000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01456-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce the notion of \(\mathbb {P}\)-subnormal subgroup in a finite group, which generalizes the one of subnormal subgroup. We prove an analogous of the well-known Jordan–Hölder Theorem for these subgroups and their related chains of subgroups.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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