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.

By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a oneobject 2-group. By a permutation 2-group we mean the 2-group Sym(G) of self-equivalences of a groupoid G and natural isomorphisms between them, with the product given by composition of self-equivalences. These generalize the ...

Within the usual semidirect product S ∗ T of regular semigroups S and T lies the set Reg (S ∗ T ) of its regular elements. Whenever S or T is completely simple, Reg (S ∗T ) is a (regular) subsemigroup. It is this ‘product’ that is the theme of the paper. It is best studied within the framework of existence (or e-) varieties of regular semigroups. Given two such classes, U and V, the e-variety U...

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding 'imprimitive wreath decomposition concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The r...

Wreath product group based spectral analysis has led to the development of the wreath product transform, a new multiresolution transform closely related to the wavelet transform. In this work, we derive the lter bank implementation of a simple wreath product transform and show that it is in fact, a multiresolution Roberts Cross edge detector. We also derive the relationship between this transfo...

In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under...

In this paper, we prove that the Birget-Rhodes expansion G̃R of a group G is not a semidirect product of a semilattice by a group but it can be nicely embedded into such a semidirect product.