J Austral Math Soc Ser A 59 pp28--609, 1995.
(Received 24 July 1992; revised 6 November 1992)
A common generalization of the author's embedding theorem concerning the E-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an orthogroup K by a group, can be embedded into a semidirect product of an orthogroup K' by a group, where K' belongs to the variety of orthogroups generated by K. The proof is based on a criterion of embeddability into a semidirect product of an orthodox semigroup by a group and uses bilocality of orthogroup bivarieties.
1991 AMS Subject Classification: 20M10, 20M19
Last Modified: Thu Jan 9 9:04:24 2003