We consider wreath product decompositions for semigroups of triangular matrices. We exhibit an explicit wreath product decomposition for the semigroup of all n× n upper triangular matrices over a given field k, in terms of aperiodic semigroups and affine groups over k. In the case that k is finite this decomposition is optimal, in the sense that the number of group terms is equal to the group c...

We construct the representations of Cayley graphs of wreath products using finite automata, pushdown automata and nested stack automata. These representations are in accordance with the notion of Cayley automatic groups introduced by Kharlampovich, Khoussainov and Miasnikov and its extensions introduced by Elder and Taback. We obtain the upper and lower bounds for a length of an element of a wr...

In this paper, two methods are described, by means of which it is possible to calculate the non rigid group of molecules consisting of a number of XH3 groups attached to a rigid framework. The first method is a combination of the wreath product formalism of Balasubramanian and modern computer algebra and the second method is a computational approach by using group theory package GAP. We apply t...

A permutation group is innately transitive if it has a transitive minimal normal subgroup, and this subgroup is called a plinth. In this paper we study three special types of inclusions of innately transitive permutation groups in wreath products in product action. This is achieved by studying the natural Cartesian decomposition of the underlying set that correspond to the product action of a w...

This paper is based on an hour address given at the Sixth Conference on Formal Power Series and Algebraic Combinatorics, held at DIMACS in 1994. It is written primarily for an audience of combinatorialists. Our hope is to publicise some intriguing enumerative conjectures which arise in the study of the homology representations of the poset of (set) partitions with an even number of blocks. The ...

A semigroup variety is called a Cross variety if it is finitely based, is generated by a finite semigroup, and has a finite lattice of subvarieties. It is established in which cases the wreath product of two semigroup varieties each of which is an atom of the lattice of semigroup varieties is a Cross variety. Furthermore, for all the pairs of atoms U and V for which this is possible, either a f...