Fibonacci length and efficiency in group presentations
Abstract
In this thesis we shall consider two topics that are contained in combinatorial group theory and concern properties of finitely presented groups. The first problem we examine is that of calculating the Fibonacci length of certain families of finitely presented groups. In pursuing this we come across ideas and unsolved problems from number theory. We mainly concentrate on finding the Fibonacci length of powers of dihedral groups, certain Fibonacci groups and a family of metacyclic groups. The second problem we investigate in this thesis is finding if the group PGL(2, p), for p a prime, is efficient on a minimal generating set. We find various presentations that define PGL(2,p) or C₂ x PSL(2,p) and direct products of these groups. As in the previous sections we come across number theoretic problems. We also have occasion to use results from tensor theory and homological algebra in order to obtain our results.
Type
Thesis, PhD Doctor of Philosophy
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.