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dc.contributor.advisorMitchell, James David
dc.contributor.advisorRuškuc, Nik
dc.contributor.authorCraik, Simon
dc.coverage.spatialiii, 198en_US
dc.description.abstractThe aim of this thesis is to understand the algebraic structure of a semigroup by studying the geometric properties of its Cayley graph. We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopfs Theorem, stating that a group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups. We classify all semigroups with one end and make use of this classification to prove various finiteness properties for semigroups with one end. We also consider the ends of digraphs with certain algebraic properties. We prove that two quasi-isometric digraphs have isomorphic end sets. We also prove that vertex transitive digraphs have 1, 2 or infinitely many ends and construct a topology that reflects the properties of the ends of a digraph.en_US
dc.publisherUniversity of St Andrews
dc.subject.lcshDirected graphsen_US
dc.titleEnds of semigroupsen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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