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Title: Semigroup presentations
Author: Ruskuc, Nikola
ISNI:       0000 0001 2445 1664
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 1995
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In this thesis we consider in detail the following two fundamental problems for semigroup presentations: 1. Given a semigroup find a presentation defining it. 2. Given a presentation describe the semigroup defined by it. We also establish two links between these two approaches: semigroup constructions and computational methods. After an introduction to semigroup presentations in Chapter 3, in Chapters 4 and 5 we consider the first of the two approaches. The semigroups we examine in these two chapters include completely O-simple semigroups, transformation semigroups, matrix semigroups and various endomorphism semigroups. In Chapter 6 we find presentations for the following semi group constructions: wreath product, Bruck-Reilly extension, Schiitzenberger product, strong semilattices of monoids, Rees matrix semigroups, ideal extensions and subsemigroups. We investigate in more detail presentations for subsemigroups in Chapters 7 and 10, where we prove a number of Reidemeister-Schreier type results for semigroups. In Chapter 9 we examine the connection between the semi group and the group defined by the same presentation. The general results from Chapters 6, 7, 9 and 10 are applied in Chapters 8, 11, 12 and 13 to subsemigroups of free semigroups, Fibonacci semigroups, semigroups defined by Coxeter type presentations and one relator products of cyclic groups. Finally, in Chapter 14 we describe the Todd-Coxeter enumeration procedure and introduce three modifications of this procedure.
Supervisor: Howie, John M. ; Robertson, Edmund F. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA171.S3R9 ; Group theory ; Representations of groups ; Semigroups