Cevik, Ahmet Sinan
(1997)
Minimality of Group and Monoid Presentations.
PhD thesis, University of Glasgow.
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Abstract
In Chapter 1 of this thesis we review existing theory concerning group and monoid presentations, and the concept of pictures over these. We also recall aspherical, combinatorial aspherical, nCockcroft (n ∈ Z+), efficient and inefficient presentations. Minimality is the final concept introduced in this chapter: we present an important theorem, due to Lustig in the case of groups and to Pride for monoids. In Chapter 2 we prove necessary and sufficient conditions for the presentation of the central extension to be pCockcroft (p a prime or 0). The starting point of this result is the joint paper of BaikHarlanderPride. We end the chapter by giving some examples. In Chapter 3 we prove a theorem on the efficiency of standard wreath products of two finite groups. We also present some applications of the theorem and end by giving examples. Chapter 4 sees discussion on the semidirect product of any two monoids. In particular we prove necessary and sufficient conditions for the standard presentation of the semidirect product of any two monoids to be pCockcroft (p a prime or 0). We end by giving some applications of this theorem to the direct product of two monoids and the semidirect product of two finite cyclic monoids. We begin Chapter 5 with an application of the main theorem of Chapter 4, namely we give necessary and sufficient conditions for a presentation of the semidirect product of a onerelator monoid by an infinite cyclic monoid to be pCockcroft (p a prime or 0), and give some examples of this. Following this we present the main theorem of this chapter, which is sufficient conditions for the presentation of a semidirect product of a onerelator monoid by an infinite cyclic monoid to be minimal but inefficient. We end by giving some examples.
Item Type: 
Thesis
(PhD)

Qualification Level: 
Doctoral 
Additional Information: 
Adviser: S J Pride 
Keywords: 
Mathematics 
Date of Award: 
1997 
Depositing User: 
Enlighten Team

Unique ID: 
glathesis:199776450 
Copyright: 
Copyright of this thesis is held by the author. 
Date Deposited: 
19 Nov 2019 14:19 
Last Modified: 
19 Nov 2019 14:19 
URI: 
http://theses.gla.ac.uk/id/eprint/76450 
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