Abstract
Throughout this paper our study focuses on transformation semigroups. These kinds of semigroups are the corner stone of semigroup theory. This is because every semigroup is isomorphic to transformation semigroup. The (total) transformation monoid TXn on a finite set Xn = {1, 2, …, n} where n ≥ 0 , n ∈ Z , is a semigroup of mapping that takes a set Xn into itself, under the operation of composition of mapping with identity IXn . In this paper, we use an algebraic method for considering the monoid T(Fl)n(G) , where an independence algebra (Fl)n(G) is a disjointed union of sets of the form Gxi for all 1 ≤ i ≤ n. Firstly, particular attention is paid to find the isomorphism between T(Fl)n(G) and the endomorphism monoid End(Fℓ)n(G). Secondly, the embeddedness of T(Fl)n(G) in (full) wreath product of Tn by Gn has been found. Finally, the description of Green's relation of T(Fl)n(G) has been provided.