Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.748128
Title: Composition of permutation representations of triangle groups
Author: Mazhar, Siddiqua
ISNI:       0000 0004 7233 2100
Awarding Body: Newcastle University
Current Institution: University of Newcastle upon Tyne
Date of Award: 2017
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Abstract:
A triangle group is denoted by (p, q, r) and has finite presentation (p, q, r) = hx, y|xp = yq = (xy)r = 1i. In the 1960’s Higman conjectured that almost every triangle group has among its homomorphic images all but finitely many of the alternating groups. This was proved by Everitt in [6]. In this thesis, we combine permutation representations using the methods used in the proof of Higman’s conjecture. We do some experiments by using GAP code and then we examine the situations where the composition of a number of coset diagrams for a triangle group is imprimitive. Chapter 1 provides the introduction of the thesis. Chapter 2 contains some basic results from group theory and definitions. In Chapter 3 we describe our construction that builds compositions of coset diagrams. In Chapter 4 we describe three situations that make the composition of coset diagrams imprimitive and prove some results about the structure of the permutation groups we construct. We conduct experiments based on the theorems we proved and analyse the experiments. In Chapter 5 we prove that if a triangle group G has an alternating group as a finite quotient of degree deg > 6 containing at least one handle, then G has a quotient Cdeg−1 p o Adeg. We also prove that if, for an integer m 6= deg − 1 such that m > 4 and the alternating group Am can be generated by two product of disjoint p-cycles, and a triangle group G has a quotient Adeg containing two disjoint handles, then G also has a quotient Am o Adeg.
Supervisor: Not available Sponsor: Faculty for the Future, Schlumberger Foundation
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.748128  DOI: Not available
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