{"title":"S.I.Adian的无限基变种的自由群的有限子群","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":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"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\":\" \",\"pages\":\"\"},\"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}","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}
Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian
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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