Now showing items 1-20 of 39

  • Adventures in applying iteration lemmas 

    Pfeiffer, Markus Johannes (University of St Andrews, 2013-06-28) - Thesis
    The word problem of a finitely generated group is commonly defined to be a formal language over a finite generating set. The class of finite groups has been characterised as the class of finitely generated groups that ...
  • Aspects of order and congruence relations on regular semigroups 

    Gomes, Gracinda Maria dos Santos (University of St Andrews, 1983) - Thesis
    On a regular semigroup S natural order relations have been defined by Nambooripad and by Lallement. Different characterisations and relationships between the Nambooripad order J, Lallement's order λ and a certain relation ...
  • Cayley automaton semigroups 

    McLeman, Alexander Lewis Andrew (University of St Andrews, 2015-06-26) - Thesis
    Let S be a semigroup, C(S) the automaton constructed from the right Cayley graph of S with respect to all of S as the generating set and ∑(C(S)) the automaton semigroup constructed from C(S). Such semigroups are ...
  • Classification and enumeration of finite semigroups 

    Distler, Andreas (University of St Andrews, 2010-06-23) - Thesis
    The classification of finite semigroups is difficult even for small orders because of their large number. Most finite semigroups are nilpotent of nilpotency rank 3. Formulae for their number up to isomorphism, and up ...
  • A commutative noncommutative fractal geometry 

    Samuel, Anthony (University of St Andrews, 2010) - Thesis
    In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained. Firstly, starting with Connes' spectral triple for a non-empty ...
  • Constructing 2-generated subgroups of the group of homeomorphisms of Cantor space 

    Hyde, James Thomas (University of St Andrews, 2017) - Thesis
    We 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 ...
  • Dimension and measure theory of self-similar structures with no separation condition 

    Farkas, Ábel (University of St Andrews, 2015-11-30) - Thesis
    We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any ...
  • Dimension theory and fractal constructions based on self-affine carpets 

    Fraser, Jonathan M. (University of St Andrews, 2013-11-29) - Thesis
    The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention ...
  • Dimension theory of random self-similar and self-affine constructions 

    Troscheit, Sascha (University of St Andrews, 2017-06-23) - Thesis
    This thesis is structured as follows. Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory. In Chapter 2 we give ...
  • Directed graph iterated function systems 

    Boore, Graeme C. (University of St Andrews, 2011-11-30) - Thesis
    This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed ...
  • Dots and lines : geometric semigroup theory and finite presentability 

    Awang, Jennifer S. (University of St Andrews, 2015-06-26) - Thesis
    Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. ...
  • Endomorphisms of Fraïssé limits and automorphism groups of algebraically closed relational structures 

    McPhee, Jillian Dawn (University of St Andrews, 2012-11-30) - Thesis
    Let Ω be the Fraïssé limit of a class of relational structures. We seek to answer the following semigroup theoretic question about Ω. What are the group H-classes, i.e. the maximal subgroups, of End(Ω)? Fraïssé limits for ...
  • Ends of semigroups 

    Craik, Simon (University of St Andrews, 2013) - Thesis
    The 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. ...
  • Finiteness conditions for unions of semigroups 

    Abu-Ghazalh, Nabilah Hani (University of St Andrews, 2013-06-28) - Thesis
    In this thesis we prove the following: The semigroup which is a disjoint union of two or three copies of a group is a Clifford semigroup, Rees matrix semigroup or a combination between a Rees matrix semigroup and a ...
  • Flatness, extension and amalgamation in monoids, semigroups and rings 

    Renshaw, James Henry (University of St Andrews, 1986) - Thesis
    We begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in ...
  • Generalized Bernstein polynomials and total positivity 

    Oruç, Halil (University of St Andrews, 1999) - Thesis
    "This thesis submitted for Ph.D. degree deals mainly with geometric properties of generalized Bernstein polynomials which replace the single Bernstein polynomial by a one-parameter family of polynomials. It also provides ...
  • Generating "large" subgroups and subsemigroups 

    Jonušas, Julius (University of St Andrews, 2016) - Thesis
    In this thesis we will be exclusively considering uncountable groups and semigroups. Roughly speaking the underlying problem is to find “large” subgroups (or subsemigroups) of the object in question, where we consider ...
  • Generating uncountable transformation semigroups 

    Péresse, Yann (University of St Andrews, 2009) - Thesis
    We consider naturally occurring, uncountable transformation semigroups S and investigate the following three questions. (i) Is every countable subset F of S also a subset of a finitely generated subsemigroup of S? If so, ...
  • Generation problems for finite groups 

    McDougall-Bagnall, Jonathan M. (University of St Andrews, 2011-11-30) - Thesis
    It can be deduced from the Burnside Basis Theorem that if G is a finite p-group with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A ...
  • The geometry of self-affine fractals 

    Miao, Jun Jie (University of St Andrews, 2008) - Thesis
    In this thesis we study the dimension theory of self-affine sets. We begin by introducing a number of notions from fractal geometry, in particular, dimensions, measure properties and iterated functions systems. We give ...