全变换半群T_(n)的极大(完全)独立子半群  

Maximal(Completely)Isolated Subsemigroups of the Full Transformation Semigroup T_(n)

作　　者：余江慧 肖坚 罗永贵 YU Jiang-hui;XIAO Jian;LUO Yong-gui(College of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《数学的实践与认识》2023年第10期210-217,共8页Mathematics in Practice and Theory

基　　金：贵州师范大学学术新苗基金项目(黔师新苗[2021]B08号)。

摘　　要：设T_(n)和S_(n)分别是有限集X_(n)=[1,2,…,n]上的全变换半群和对称群.通过分析半群T_(n)的格林关系及生成关系,获得了半群T_(n)的(完全)独立子半群的完全分类.进一步,证明了半群T_(n)的极大独立子半群与极大完全独立子半群是一致的.Let Sn and Tn be symmetric group and the full transformation semigroup on the finite set X_(n)={1,2,…,n},respectively.By analyzing the Green's relation and generative relation of the full transformation semigroup Tn,the complete classification of the(completely)isolated subsemigroup of T_(n) is obtained.Further,the coincide of maximal isolated subsemigroups and maximal completely isolated subsemigroups of T_(n) be proved.

关 键 词：全变换半群 对称群 生成关系 极大独立子半群 极大完全独立子半群 

分 类 号：O152.7[理学—数学]