{"title":"Properties of gyrogroups induced by groups whose central quotients being 2-Engel","authors":"Jaturon Wattanapan, T. Suksumran","doi":"10.55730/1300-0098.3531","DOIUrl":null,"url":null,"abstract":": A group Γ is said to be CCII if the quotient Γ /Z (Γ) is 2 -Engel or, equivalently, commutator-inversion invariant, where Z (Γ) is the center of Γ . In this article, we prove algebraic and topological properties of gyrogroups that are induced by CCII groups. Then, using a classification of non-abelian groups of order n with n < 32 , we determine all finite CCII groups of order less than 32 .","PeriodicalId":0,"journal":{"name":"","volume":"46 s161","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.55730/1300-0098.3531","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
: A group Γ is said to be CCII if the quotient Γ /Z (Γ) is 2 -Engel or, equivalently, commutator-inversion invariant, where Z (Γ) is the center of Γ . In this article, we prove algebraic and topological properties of gyrogroups that are induced by CCII groups. Then, using a classification of non-abelian groups of order n with n < 32 , we determine all finite CCII groups of order less than 32 .
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