On iterated semidirect products of finite semilattices

Homology of Iterated Semidirect Products of Free Groups

Let G be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of G. This resolution is used to define representations of groups which act compatibly on G, generalizing classical constructions of Magnus, Burau, and Gassner. Our construction also yields algorithms for comp...

Semidirect Products With the Pseudovariety of All Finite Groups

On the second cohomology of semidirect products

Let G be a group which is the semidirect product of a normal subgroup N and a subgroup T , and let M be a G-module with not necessarily trivial G-action. Then we embed the simultaneous restriction map res = (resN , res G T ) t : H2(G,M) → H2(N,M)T × H2(T,M) into a natural five term exact sequence consisting of one and two-dimensional cohomology groups of the factors N and T . The elements of H2...

Equations on Semidirect Products of Commutative Semigroups

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 ∈ ,...

Semidirect Products of Ordered Semigroups