Now showing items 1-16 of 16

  • 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 ...
  • 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 ...
  • 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 ...
  • 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, ...
  • Graph automatic semigroups 

    Carey, Rachael Marie (University of St Andrews, 2016-06-24) - Thesis
    In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups. We consider the properties of graph ...
  • On defining groups efficiently without using inverses 

    Campbell, Colin Matthew; Mitchell, James David; Ruskuc, Nikola (2002-07) - Journal article
    Let G be a group, and let <A \ R> be a finite group presentation for G with \R\ greater than or equal to \A\. Then there exists a, finite semigroup, presentation <B \ Q> for G such that \Q\ - \B\ = \R\ - \A\. Moreover, B ...
  • On generators, relations and D-simplicity of direct products, Byleen extensions, and other semigroup constructions 

    Baynes, Samuel (University of St Andrews, 2015-11-30) - Thesis
    In 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 ...
  • Semigroup presentations 

    Ruškuc, Nik (University of St Andrews, 1995) - Thesis
    In this thesis we consider in detail the following two fundamental problems for semigroup presentations: 1. Given a semigroup find a presentation defining it. 2. Given a presentation describe the semigroup defined by ...
  • Topics in combinatorial semigroup theory 

    Maltcev, Victor (University of St Andrews, 2012-11-30) - Thesis
    In this thesis we discuss various topics from Combinatorial Semigroup Theory: automaton semigroups; finiteness conditions and their preservation under certain semigroup theoretic notions of index; Markov semigroups; ...
  • Unary FA-presentable semigroups 

    Cain, Alan James; Ruskuc, Nik; Thomas, R.M. (2012-06-08) - Journal article
    Automatic presentations, also called FA-presentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has ...