{"title":"Maximal Subgroups of Almost Subnormal Subgroups in Division Rings","authors":"Bui Xuan Hai","doi":"10.1007/s40306-021-00456-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate maximal subgroups of an almost subnormal subgroup <i>G</i> in a division ring <i>D</i> whose center is infinite. Among results, we prove that if <i>M</i> is such a maximal subgroup, then <i>M</i> is abelian provided <i>M</i> is either locally finite or <i>FC</i>-group, and <i>D</i> is weakly locally finite. Also, we prove a theorem on the existence of non-cyclic free subgroups of a maximal subgroup <i>M</i> in such a <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-021-00456-9.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-021-00456-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate maximal subgroups of an almost subnormal subgroup G in a division ring D whose center is infinite. Among results, we prove that if M is such a maximal subgroup, then M is abelian provided M is either locally finite or FC-group, and D is weakly locally finite. Also, we prove a theorem on the existence of non-cyclic free subgroups of a maximal subgroup M in such a G.
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.