CONJUGACY CLASSES OF THE ORDER-PRESERVING AND ORDER-DECREASING PARTIAL ONE-TO-ONE TRANSFORMATION SEMIGROUPS

Abstract

In this paper ą is considered to be the partial one-to-one transformation semigroup on X n = {1,2,L,n}. The order-preserving and order-decreasing partial one-to-one transformation semigroup ą1 ) is defined to be the subsemigroups of ą . The nilpotent and idempotent elements of ą1 were then obtained from its conjugacy classes using path structure to be n+1 and *恼馁жi − ж 2 respectively. The index and period of each conjugacy classes were also found. More so, some properties of conjugacy classes were stated.