Computing presentations for finite soluble groups
Date
1993
Authors
Niemeyer, Alice C
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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.
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Thesis (PhD)
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