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dc.contributor.advisorBleak, Collin Patrick
dc.contributor.advisorRuškuc, Nik
dc.contributor.authorHyde, James Thomas
dc.coverage.spatialvi, 141 leavesen_US
dc.description.abstractWe study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the group of homeomorphisms of Cantor space. In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we study vigorous subgroups of H[sub]c. A subgroup G of H[sub]c is vigorous if for any non-empty clopen set A with proper non-empty clopen subsets B and C there exists g ∈ G with supp(g) ⊑ A and Bg ⊆ C. It is a corollary of the main theorem of Chapter 3 that all finitely generated simple vigorous subgroups of H[sub]c are in fact 2-generated. We show the family of finitely generated, simple, vigorous subgroups of H[sub]c is closed under several natural constructions. In Chapter 4 we use a generalised notion of word and the tight completion construction from [13] to construct a family of subgroups of H[sub]c which generalise Thompson's group V . We give necessary conditions for these groups to be finitely generated and simple. Of these we show which are vigorous. Finally we give some examples.en_US
dc.publisherUniversity of St Andrews
dc.subject.lcshGroup theoryen
dc.subject.lcshCantor setsen
dc.titleConstructing 2-generated subgroups of the group of homeomorphisms of Cantor spaceen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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