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|Title: ||Semigroup presentations|
|Authors: ||Ruškuc, Nik|
|Supervisors: ||Howie, John M.|
Robertson, E. F.
|Issue Date: ||1995|
|Abstract: ||In this thesis we consider in detail the following two fundamental problems for
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.|
|Publisher: ||University of St Andrews|
|Appears in Collections:||Pure Mathematics Theses|
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