Mahdavi Soheila, Ashrafi Ali-Reza, Salahshour Mohammad A.
{"title":"Normal subgyrogroups of certain gyrogroups","authors":"Mahdavi Soheila, Ashrafi Ali-Reza, Salahshour Mohammad A.","doi":"10.56415/qrs.v30.09","DOIUrl":null,"url":null,"abstract":"Suppose that (T;*) is a groupoid with a left identity such that each element a 2 T has a left inverse. Then T is called a gyrogroup if and only if (i) there exists a function gyr : T x T -Aut(T) such that for all a; b; c 2 T, a * (b * c) = (a * b) ? gyr[a; b]c, where gyr[a; b]c = gyr(a; b)(c); and (ii) for all a; b 2 T, gyr[a; b] = gyr[a ? b; b]. In this paper, the structure of normal subgyrogroups of certain gyrogroups are investigated.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.09","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: 1
Abstract
Suppose that (T;*) is a groupoid with a left identity such that each element a 2 T has a left inverse. Then T is called a gyrogroup if and only if (i) there exists a function gyr : T x T -Aut(T) such that for all a; b; c 2 T, a * (b * c) = (a * b) ? gyr[a; b]c, where gyr[a; b]c = gyr(a; b)(c); and (ii) for all a; b 2 T, gyr[a; b] = gyr[a ? b; b]. In this paper, the structure of normal subgyrogroups of certain gyrogroups are investigated.
假设(T;*)是一个具有左单位元的群,使得2t的每个元素都有一个左逆。那么当且仅当(i)存在一个函数gyr: T x T -Aut(T)使得对于所有a;b;c2t, a * (b * c) = (a * b)gyr[一个;c, where gyr[a];B]c = gyr(a;b) (c);(ii)所有a;b 2 T, gyr[a;B] = gyr[a] ?b;b]。本文研究了某些陀螺群的正规子陀螺群的结构。