Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497710
Title: Presentations and efficiency of semigroups
Author: Ayik, Hayrullah
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 1998
Availability of Full Text:
Access from EThOS:
Access from Institution:
Abstract:
In this thesis we consider in detail the following two problems for semigroups: (i) When are semigroups finitely generated and presented? (ii) Which families of semigroups can be efficiently presented? We also consider some other finiteness conditions for semigroups, homology of semigroups and wreath product of groups. In Chapter 2 we investigate finite presentability and some other finiteness conditions for the O-direct union of semigroups with zero. In Chapter 3 we investigate finite generation and presentability of Rees matrix semigroups over semigroups. We find necessary and sufficient conditions for finite generation and presentability. In Chapter 4 we investigate some other finiteness conditions for Rees matrix semigroups. In Chapter 5 we consider groups as semigroups and investigate their semigroup efficiency. In Chapter 6 we look at "proper" semigroups, that is semigroups that are not groups. We first give examples of efficient and inefficient "proper" semigroups by computing their homology and finding their minimal presentations. In Chapter 7 we compute the second homology of finite simple semigroups and find a "small" presentation for them. If that "small" presentation has a special relation, we prove that finite simple semigroups are efficient. Finally, in Chapter 8, we investigate the efficiency of wreath products of finite groups as groups and as semigroups. We give more examples of efficient groups and inefficient groups.
Supervisor: Campbell, C. M. ; O'Connor, J. J. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.497710  DOI: Not available
Keywords: QA171.S3A9 ; Group theory ; Representations of groups
Share: