This paper is the culmination of a series of work integrating syntactic and global semigroup theoretical approaches for the purpose of calculating semidirect products of pseudovarieties of semigroups. We introduce various abstract and algorithmic properties that a pseudovariety of semi-groups might possibly satisfy. The main theorem states that given a nite collection of pseudovarieties, each s...

Abstract The semidirect product of a finitely generated group dual with the symmetric can be described through so-called group-theoretical categories partitions (covers only special case; due to Raum–Weber, 2015) and skew (more general; Maaßen, 2018). We generalize these results case graph categories, which allows replace by automorphisms some graph.

The Garside group, as a generalization of braid groups and Artin groups of finite types, is defined as the group of fractions of a Garside monoid. We show that the semidirect product of Garside monoids is a Garside monoid. We use the semidirect product Z ⋉ G of the infinite cyclic group Z and the cartesian product G of a Garside group G to study the properties of roots and powers of elements in...

In this paper; we study equations on semidirect products of commutative semigroups. Let Comq,r denote the pseudovariety of all finite semigroups that satisfy the equations xy = yx and x r + q = xr. The pseudovariety Com1,1 is the pseudovariety of all finite semilattices. We consider the product pseudovariety Comq,r * generated by all semidirect products of the form S*T with S ∈ Comq,r and T ∈ ,...