{"title":"An Example of a Relatively Maximal Nonpronormal Subgroup of Odd Order in a Finite Simple Group","authors":"X. Zhang, L. Su, D. O. Revin","doi":"10.1134/s0037446624030133","DOIUrl":null,"url":null,"abstract":"<p>We prove the existence of a triple <span>\\( ({\\mathfrak{X}},G,H) \\)</span>, where <span>\\( {\\mathfrak{X}} \\)</span>\nis a class of finite groups consisting of groups of odd order which is complete\n(i.e., closed under subgroups, homomorphic images, and extensions),\n<span>\\( G \\)</span> is a finite simple group, <span>\\( H \\)</span> is an <span>\\( {\\mathfrak{X}} \\)</span>-maximal subgroup in <span>\\( G \\)</span>,\nand <span>\\( H \\)</span> is not pronormal in <span>\\( G \\)</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"18 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446624030133","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
Abstract
We prove the existence of a triple \( ({\mathfrak{X}},G,H) \), where \( {\mathfrak{X}} \)
is a class of finite groups consisting of groups of odd order which is complete
(i.e., closed under subgroups, homomorphic images, and extensions),
\( G \) is a finite simple group, \( H \) is an \( {\mathfrak{X}} \)-maximal subgroup in \( G \),
and \( H \) is not pronormal in \( G \).
我们证明了三元组 \( ({\mathfrak{X}},G,H) \)的存在,其中 \( {\mathfrak{X}} \)是一类由奇数阶群组成的有限群,它是完全的(即、是一个有限单群,\( H \)是\( G \)中的\( {\mathfrak{X}} \)-最大子群,并且\( H \)在\( G \)中不是代规范的。
期刊介绍:
Siberian Mathematical Journal is journal published in collaboration with the Sobolev Institute of Mathematics in Novosibirsk. The journal publishes the results of studies in various branches of mathematics.