Now showing items 1-20 of 24

    • 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 ...
    • Automatic S-acts and inverse semigroup presentations 

      Dombi, Erzsebet Rita (University of St Andrews, 2005) - Thesis
      To provide a general framework for the theory of automatic groups and semigroups, we introduce the notion of an automatic semigroup act. This notion gives rise to a variety of definitions for automaticity depending on the ...
    • Automatic semigroups : constructions and subsemigroups 

      Descalco, L. (University of St Andrews, 2002) - Thesis
      In this thesis we start by considering conditions under which some standard semigroup constructions preserve automaticity. We first consider Rees matrix semigroups over a semigroup, which we call the base, and work on the ...
    • 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 ...
    • Computational techniques in finite semigroup theory 

      Wilson, Wilf A. (University of St Andrews, 2019-06-25) - Thesis
      A semigroup is simply a set with an associative binary operation; computational semigroup theory is the branch of mathematics concerned with developing techniques for computing with semigroups, as well as investigating ...
    • Computing finite semigroups 

      East, James; Egri-Nagy, Attila; Mitchell, James D.; Péresse, Yann (2018-02-14) - Journal article
      Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples ...
    • 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 ...
    • On plausible counterexamples to Lehnert's conjecture 

      Bennett, Daniel (University of St Andrews, 2018) - Thesis
      A group whose co-word problem is a context free language is called co𝐶𝐹 . Lehnert's conjecture states that a group 𝐺 is co𝐶𝐹 if and only if 𝐺 embeds as a finitely generated subgroup of R. Thompson's group V . In this ...
    • Presentations for subsemigroups of groups 

      Cain, Alan James (University of St Andrews, 2005) - Thesis
      This thesis studies subsemigroups of groups from three perspectives: automatic structures, ordinary semigroup presentations, and Malcev presentaions. [A Malcev presentation is a presentation of a special type for a semigroup ...
    • Semigroup congruences : computational techniques and theoretical applications 

      Torpey, Michael (University of St Andrews, 2019-06-25) - Thesis
      Computational semigroup theory is an area of research that is subject to growing interest. The development of semigroup algorithms allows for new theoretical results to be discovered, which in turn informs the creation ...