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dc.contributor.advisorRuškuc, Nik
dc.contributor.authorBaynes, Samuel
dc.coverage.spatialvi, 146 p.en_US
dc.date.accessioned2015-10-08T09:19:34Z
dc.date.available2015-10-08T09:19:34Z
dc.date.issued2015-11-30
dc.identifieruk.bl.ethos.667526
dc.identifier.urihttp://hdl.handle.net/10023/7629
dc.description.abstractIn this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a D-simple finitely presentable semigroup. We consider some well-known semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be D-simple and a very strong necessary condition for an extension to be finitely presentable. The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.en_US
dc.language.isoenen_US
dc.publisherUniversity of St Andrews
dc.subjectSemigroupsen_US
dc.subjectD-simpleen_US
dc.subjectBisimpleen_US
dc.subjectByleen extensionen_US
dc.subjectRelative ranken_US
dc.subjectEmbeddingen_US
dc.subject.lccQA182.B2
dc.subject.lcshSemigroupsen_US
dc.subject.lcshGroup theory--Generatorsen_US
dc.subject.lcshGroup theory--Relationsen_US
dc.subject.lcshEmbeddings (Mathematics)en_US
dc.titleOn generators, relations and D-simplicity of direct products, Byleen extensions, and other semigroup constructionsen_US
dc.typeThesisen_US
dc.type.qualificationlevelDoctoralen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US


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