3 research outputs found
Computing presentations for finite soluble groups
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