On transformations of index $1$
Leyla BUGAY, Osman Kelekci̇ · TURKISH JOURNAL OF MATHEMATICS · 2014
The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that a^{m+r}=a^m, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T_n, which we call transformations of index 1.