M. Petrich et al., THE SYNTACTIC MONOID OF THE SEMIGROUP GENERATED BY A MAXIMAL PREFIX CODE, Proceedings of the American Mathematical Society, 124(3), 1996, pp. 655-663
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.