Some New Monoid and Group Constructions Under Semidirect Products

Abstract

In this paper, we mainly define a semidirect product version of the Schützenberger 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 Schützenberger products and the subgroup separability for this new two-sided semidirect product.