Bilateral semidirect product decompositions of transformation monoids

Semidirect Product Decompositions of Ordered Groupoids and Inverse Semigroups

Semidirect Products and Wreath Products of Strongly Π-inverse Monoids

In this paper we determine the necessary and sufficient conditions for the semidirect products and the wreath products of two monoids to be strongly π-inverse. Furthermore, we determine the least group congruence on a strongly π-inverse monoid, and we give some important isomorphism theorems.

Semidirect product decomposition of Coxeter groups

Let (W,S) be a Coxeter system, let S = I ∪ J be a partition of S such that no element of I is conjugate to an element of J , let J̃ be the set of WI -conjugates of elements of J and let W̃ be the subgroup of W generated by J̃ . We show that W = W̃ ⋊WI and that J̃ is the canonical set of Coxeter generators of the reflection subgroup W̃ of W . We also provide algebraic and geometric conditions for an e...

On generalized semidirect product of association schemes

In this paper, we introduce a new product operation of association schemes in order to generalize the notion of semidirect products and wreath product. We then show that our construction covers some association schemes which are neither wreath products nor semidirect products of two given association schemes.

Complexity Analysis: Finite Transformation Monoids

We examine the computational complexity of some problems from algebraic automata theory and from the field of communication complexity: testing Green’s relations (relations that are fundamental in monoid theory), checking the property of a finite monoid to have only Abelian subgroups, and determining the deterministic communication complexity of a regular language. By well-known algebraizations...