Some new monoid and group constructions under semidirect products

Abstract

In this paper we mainly define semidirect product version of the Schutzenberger product and also a new two-sided semidirect product construction for arbitrary two monoids. Then, as main results, we present a generating and a relator set for these two products. Additionally, to explain why these products have been defined, we investigate the regularity for the semidirect product version of Schutzenberger products and the subgroup separability for this new two-sided semidirect product.