交叉*正则半群与二面体群之间的关系（英文）

THE RELATIONSHIP BETWEEN CROSS*-REGULAR SEMIGROUPS AND DIHEDRAL GROUPS

我们介绍了交叉*正则半群,这个概念是对正则半群的推广·通过应用该概念,我们证明了交叉*正则半群的一些元素属于二面体群,并且还证明了:若D_(2n)×D_(2m)是由两个元素生成的,则m,n是奇数(n,m> 2)而且D_(2n)×D_(2m)同构于一个交叉*正则半群.

We introduce the concept of cross*-regular semigroups which is a general-ization of regular semigroups.By applying the cross*-regularity of semigroups,we show that some elements of cross*-regular semigroups belong to a dihedral group,moreover,if D2n×D2m is generated by two elements,then both n and m are odd(n,m>2),and we prove D2n×D2m≌S,where S is a cross*-regular semigroup.