On quasi-F-orthodox semigroups

Abstract

An orthodox semigroup S is termed quasi-F-orthodox if the greatest inverse semigroup homomorphic image of S1 is F-inverse. In this paper we show that each quasi-F-orthodox semigroup is embeddable into a semidirect product of a band by a group. Furthermore, we present a subclass in the class of quasi-F-orthodox semigroups whose members S are embeddable into a semidirect product of a band B by a group in such a way that B belongs to the band variety generated by the band of idempotents in S. In particular, this subclass contains the F-orthodox semigroups and the idempotent pure homomorphic images of the bifree orthodox semigroups.