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...

A construction of a minimum cycle bases for the wreath product of some classes of graphs is presented. Moreover, the basis numbers for the wreath product of the same classes are determined.

The wreath product of groups A B is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras. Consider Lie algebras H and G over a field K. Let U(G) be the universal enveloping algebra. Then H̄ = HomK(U(G), H) has the natural structure of a Lie algebra, where the multiplication is defined via the comultiplication in U(G). Also, G acts by derivations...

The Krohn-Rhodes complexity theory for pure (without lin-earity) automata is well-known. This theory uses an operation of wreath product as a decomposition tool. The main goal of the paper is to introduce the notion of complexity of linear automata. This notion is ultimately related with decompositions of linear automata. The study of these decom-positions is the second objective of the paper. ...