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Extensions of regular orthogroups by groups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Mária B. Szendrei
Mária B. Szendrei
Affiliation:
József Attila University, Bolyai Institute, 6720 Szeged, Aradi vértanúk tere 1, Hungary, email: [email protected]
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Abstract

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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.

MSC classification

Secondary: 20M10: General structure theory 20M19: Orthodox semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 28 - 60
Copyright
Copyright © Australian Mathematical Society 1995

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