On syntactic monoids of biunitary submonoids determined by homomorphisms from free semigroups onto completely simple semigroups

We deal with the maximal bifix code construction which is a natural generalization of a group code construction. For a surjective morphism ϕ from a free monoid A* onto a completely simple semigroup with an adjoined identity M(G;I,J;Σ)1 and a submonoid S of M(G;I,J;Σ)1, under certain conditions, the base of a submonoid ϕ-1(S) is a maximal bifix code X. We investigate the relationships between the surjective morphism ϕ and the syntactic monoid of the monoid generated by X.