THE SYNTACTIC MONOID OF THE SEMIGROUP GENERATED BY A MAXIMAL PREFIX CODE

In this paper we investigate the semigroup structure of the syntactic monoid Syn(C+) of C+, the semigroup generated by a maximal prefix code C for which C+ is a single class of the syntactic congruence. In arti cular we prove that for such a prefix code C, either Syn(C+) is a grou p or it is isomorphic to a special type of submonoid of G x T(R) where G is a group and T(R) is the full transformation semigroup on a set R with more than one element. From this description we conclude that Sy n(C+) has a kernel J which is a right group. We further investigate se parately the case when J is a right aero semigroup and the case when J is a group.