On transformations of index 1

The index and the period of an element a of a finite semigroup are defined as the smallest values of m ≥ 1 and r ≥ 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 Tn , which we call transformations of index 1 .