Abstract. It was recently shown in [Re] that the set of all periodic endomorphisms of a free monoid over a finite alphabet is a finite union of semigroups each of which is an ideal extension of a rectangular group by a nilpotent semigroup of finite index. It is the purpose of this paper to investigate these basic semigroups more closely to determine, among other things, the relationship between the parameters defining them and their algebraic structure. We also establish conditions for inclusion of two basic semigroups and describe a lower semilattice of the lattice of all ideals of such a semigroup.

AMS Subject Classification (1991): 20M05

Keyword(s): periodic endomorphisms of free monoids

Received November 1, 1993. (Registered under 5591/2009.)