由群和变换生成的正则半群  

Regular semigroups generated by a group and a transformation

作　　者：李旺威 黎先华 LI Wangwei;LI Xianhua(Department of Mathematics,Lingnan Normal University,Zhanjiang,Guangdong 524048,China;Department of Mathematics,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]岭南师范学院数学与统计学院,广东湛江524048 [2]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2024年第3期97-100,共4页Journal of Guizhou Normal University：Natural Sciences

基　　金：广东省基础与应用基础研究基金(2023A1515011093);岭南师范学院博士启动基金资助项目(ZL1924);岭南师范学院2023年度校级基础教育教改项目(10)。

摘　　要：设T_(n)和S_(n)分别是集合X_(n)={1,2,…,n}上的全变换半群和对称群。设K(n,r)={α∈T_(n)|rank(α)≤r},G≤S_(n)和α∈T_(n)S_(n)。借助群论专业软件GAP在前期的摸索,确定了与一类正则变换半群相对应的传递群之间的等价刻画,主要内容如下:1)对K(n,n-2)中的每一个变换α,都是正则半群时,给出了传递群G及其阶数相对应的等价刻画;2)对K(n,3)中的每一个变换α,都是正则半群时,给出了传递群G及其阶数相对应的等价刻画。Let T_(n)and S_(n)be the full transformation semigroup and the symmetric group on X_(n)={1,2,…,n},respectively.Suppose that K(n,r)={α∈T_(n)|rank(α)≤r},G≤S_(n)andα∈T_(n)\S_(n).In this paper we mainly determine the equivalent characterizations between transitive groups corresponding to a class of regular transformation semigroups by GAP.The main content is as follows:1)When<G,α>is a regular semigroup for each transformation in K(n,n-2),we give the equivalent characterizations of transitive groups and their orders;2)When<G,α>is a regular semigroup for each transformation in K(n,3),we give the equivalent characterizations of transitive groups and their orders.

关 键 词：传递群 本原群 正则半群 

分 类 号：O152.2[理学—数学]