Generalized transformation semigroups

ABSTRACT Let X and Y be two non-empty (disjoint) sets and let T(X,Y) denote the set of all (full) transformations from X to Y. For any fixed transformation θ: Y→X define a sandwich operation "*" on T(X,Y) by α*β=α∘θ∘β for all α,β∈T(X,Y). Then, the set T(X,Y) together with the sandwich operation "*" is a semigroup which is called a generalized transformation semigroup, and it is denoted by T(X,Y;θ). In this thesis we will compile some studies that contain important results about generating sets and ranks of T(X,Y;θ) and present them to the information of the researchers. Keywords: Generalized transformation semigroups, generating set, rank.