Rank of the Subsemigroup of the Semigroup of Finite Full Contraction Maps Generated by Elements of Defect One

Let Tn be the semigroup of full transformation on a nite set n. Then, a map ∈ Tn is said to be a contraction, if for all x; y ∈ Xn, |x − y| ≤ |x − y|. Let CTn denote the subsemigroup of all contraction maps in Tn. In this paper we calculated the rank of the subsemigroup of CTn generated by elements of defect one, where the defect of ∈ CTn is dened to be the cardinality of the set Xn\im(∝) and rank of a semigroup is the smallest number of generators for the semigroup.