Computing presentations for finite soluble groups

Abstract

The work in this thesis was carried out in the area of computational group theory. The latter is concerned with designing algorithm s and developing their practical implementations for investigating problem s regarding groups. An important class of groups are finite soluble groups. These can be described in a computationally convenient way by power conjugate presentations. In practice, however, they are usually supplied differently. The aim of this thesis is to propose algorithm s for computing power conjugate presentations for finite soluble groups. This is achieved in two different ways. One of the ways in which a finite soluble group is often supplied is as a quotient of a finitely presented group. T he first p art of the thesis is concerned with designing an algorithm to compute a power conjugate presentation for a finite soluble group given in this way. T he theoretical background for the algorithm is provided and its practicality is investigated on an implementation. T he second p a rt of the thesis describes the theoretical aspects of an algorithm to compute all pow er conjugate presentations for a certain class of finite soluble groups of a given order.