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dc.contributor.advisorCampbell, C. M. (Colin Matthew)
dc.contributor.advisorO'Connor, John J. (John Joseph)
dc.contributor.authorAyik, Hayrullah
dc.description.abstractIn 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.en_US
dc.publisherUniversity of St Andrews
dc.subject.lcshGroup theoryen_US
dc.subject.lcshRepresentations of groupsen_US
dc.titlePresentations and efficiency of semigroupsen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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