{"title":"c-subnormality 子群对有限群结构的影响","authors":"Dana Jaraden, Ali Ateiwi, Jehad Jaraden","doi":"10.1515/gmj-2024-2036","DOIUrl":null,"url":null,"abstract":"Let <jats:italic>H</jats:italic> be a subgroup of a group <jats:italic>G</jats:italic>. We say that <jats:italic>H</jats:italic> is <jats:italic>c</jats:italic>-subnormal in <jats:italic>G</jats:italic> if there exists a subnormal subgroup <jats:italic>T</jats:italic> of <jats:italic>G</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo></m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0064.png\"/> <jats:tex-math>{HT=G}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>∩</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>⩽</m:mo> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0065.png\"/> <jats:tex-math>{H\\cap T\\leqslant H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0073.png\"/> <jats:tex-math>{H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the maximal normal subgroup of <jats:italic>G</jats:italic> which is contained in <jats:italic>H</jats:italic>. In this paper, we investigate the structure of a finite group <jats:italic>G</jats:italic> under the assumption that all maximal subgroups are <jats:italic>c</jats:italic>-subnormal subgroups and present some new conditions for supersolvability.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The influence of c-subnormality subgroups on the structure of finite groups\",\"authors\":\"Dana Jaraden, Ali Ateiwi, Jehad Jaraden\",\"doi\":\"10.1515/gmj-2024-2036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <jats:italic>H</jats:italic> be a subgroup of a group <jats:italic>G</jats:italic>. We say that <jats:italic>H</jats:italic> is <jats:italic>c</jats:italic>-subnormal in <jats:italic>G</jats:italic> if there exists a subnormal subgroup <jats:italic>T</jats:italic> of <jats:italic>G</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo></m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2036_eq_0064.png\\\"/> <jats:tex-math>{HT=G}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>∩</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>⩽</m:mo> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2036_eq_0065.png\\\"/> <jats:tex-math>{H\\\\cap T\\\\leqslant H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2036_eq_0073.png\\\"/> <jats:tex-math>{H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the maximal normal subgroup of <jats:italic>G</jats:italic> which is contained in <jats:italic>H</jats:italic>. In this paper, we investigate the structure of a finite group <jats:italic>G</jats:italic> under the assumption that all maximal subgroups are <jats:italic>c</jats:italic>-subnormal subgroups and present some new conditions for supersolvability.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2024-2036\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2036","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
如果存在一个 G 的子正则子群 T，使得 H T = G {HT=G}，并且 H ∩ T ⩽ H G {H\cap T\leqslant H_{G}} ，我们就说 H 在 G 中是 c 正则子群。 本文研究了在所有最大子群都是 c-subnormal 子群的假设下有限群 G 的结构，并提出了一些新的超可溶条件。
The influence of c-subnormality subgroups on the structure of finite groups
Let H be a subgroup of a group G. We say that H is c-subnormal in G if there exists a subnormal subgroup T of G such that HT=G{HT=G} and H∩T⩽HG{H\cap T\leqslant H_{G}}, where HG{H_{G}} is the maximal normal subgroup of G which is contained in H. In this paper, we investigate the structure of a finite group G under the assumption that all maximal subgroups are c-subnormal subgroups and present some new conditions for supersolvability.
期刊介绍：
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.
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