{"title":"On the Kegel–Wielandt $$\\sigma$$ -Problem","authors":"","doi":"10.1134/s0081543823060093","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>For an arbitrary partition <span> <span>\\(\\sigma\\)</span> </span> of the set <span> <span>\\(\\mathbb{P}\\)</span> </span> of all primes, a sufficient condition for the <span> <span>\\(\\sigma\\)</span> </span>-subnormality of a subgroup of a finite group is given. It is proved that the Kegel–Wielandt <span> <span>\\(\\sigma\\)</span> </span>-problem has a positive solution in the class of all finite groups all of whose nonabelian composition factors are alternating groups, sporadic groups, or Lie groups of rank 1. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823060093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For an arbitrary partition \(\sigma\) of the set \(\mathbb{P}\) of all primes, a sufficient condition for the \(\sigma\)-subnormality of a subgroup of a finite group is given. It is proved that the Kegel–Wielandt \(\sigma\)-problem has a positive solution in the class of all finite groups all of whose nonabelian composition factors are alternating groups, sporadic groups, or Lie groups of rank 1.
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