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dc.contributor.advisorGrigorchuk, Rostislav
dc.creatorBenli, Mustafa G
dc.date.accessioned2013-12-16T20:01:53Z
dc.date.available2015-08-01T05:48:23Z
dc.date.created2013-08
dc.date.issued2013-07-22
dc.date.submittedAugust 2013
dc.identifier.urihttp://hdl.handle.net/1969.1/151072
dc.description.abstractThis dissertation is devoted to the study of self-similar groups and related topics. It consists of three parts. The first part is devoted to the study of examples of finitely generated amenable groups for which every finitely presented cover contains non-abelian free subgroups. The study of these examples was motivated by natural questions about finiteness properties of finitely generated groups. We show that many examples of amenable self-similar groups studied in the literature cannot be covered by finitely presented amenable groups. We investigate the class of contracting self-similar groups from this perspective and formulate a general result which is used to detect this property. As an application we show that almost all known examples of groups of intermediate growth cannot be covered by finitely presented amenable groups. The latter is related to the problem of the existence of finitely presented groups of intermediate growth. The second part focuses on the study of one important example of a self-similar group called the first Grigorchuk group G, from the viewpoint of pro finite groups. We investigate finite quotients of this group related to presentations and group (co)homology. As an outcome of this investigation we prove that the pro finite completion G_hat of this group is not finitely presented as a pro finite group. The last part focuses on a class of recursive group presentations known as L-presentations, which appear in the study of self-similar groups. We investigate the relation of such presentations with the normal subgroup structure of finitely presented groups and show that normal subgroups with finite cyclic quotient of finitely presented groups have such presentations. We apply this result to finitely presented indicable groups without free sub-semigroups.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectself-similar groups
dc.subjectpresentations
dc.subjectamenability
dc.subjectgroups of intermediate growth
dc.subjectprofinite completions
dc.subjectrecursive presentations
dc.titlePresentations and Structural Properties of Self-similar Groups and Groups without Free Sub-semigroups
dc.typeThesis
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas A & M University
thesis.degree.nameDoctor of Philosophy
thesis.degree.levelDoctoral
dc.contributor.committeeMemberButenko, Sergiy
dc.contributor.committeeMemberNekrashevych, Volodymyr
dc.contributor.committeeMemberSunic, Zoran
dc.type.materialtext
dc.date.updated2013-12-16T20:01:53Z
local.embargo.terms2015-08-01


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