{"title":"The commutator subgroup of a pair of groups","authors":"H. Arabyani","doi":"10.32513/tmj/19322008151","DOIUrl":null,"url":null,"abstract":"Schur proved that if G is a group such that G/Z(G) is finite, then G′ is finite. Several authors studied the converse of Schur’s theorem. In this paper, we extend the converse of Schur’s theorem to a pair of groups. Also, we determine the structure of a pairs of groups under some conditions.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tbilisi Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32513/tmj/19322008151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Schur proved that if G is a group such that G/Z(G) is finite, then G′ is finite. Several authors studied the converse of Schur’s theorem. In this paper, we extend the converse of Schur’s theorem to a pair of groups. Also, we determine the structure of a pairs of groups under some conditions.
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