{"title":"Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian","authors":"H. T. Aslanyan, A. Gevorgyan, H. Grigoryan","doi":"10.52737/18291163-2019.11.6-1-6","DOIUrl":null,"url":null,"abstract":"It is proved that all finite subgroups of the free groups of the infinitely based varieties of S.I. Adian are cyclic. The set of all non-isomorphic free groups of rank $m$ in this varieties is of continuum cardinality for every finite rank $m > 1$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2019.11.6-1-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
It is proved that all finite subgroups of the free groups of the infinitely based varieties of S.I. Adian are cyclic. The set of all non-isomorphic free groups of rank $m$ in this varieties is of continuum cardinality for every finite rank $m > 1$.
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