Browsing by Subject "Semigroups"
Now showing items 120 of 24

Adventures in applying iteration lemmas
(University of St Andrews, 20130628)  ThesisThe 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 Sacts and inverse semigroup presentations
(University of St Andrews, 2005)  ThesisTo 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
(University of St Andrews, 2002)  ThesisIn 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
(University of St Andrews, 20150626)  ThesisLet 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
(University of St Andrews, 20100623)  ThesisThe 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
(University of St Andrews, 20190625)  ThesisA 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
(20180214)  Journal articleUsing 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
(University of St Andrews, 20150626)  ThesisGeometric 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
(University of St Andrews, 20121130)  ThesisLet 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 Hclasses, i.e. the maximal subgroups, of End(Ω)? Fraïssé limits for ... 
Ends of semigroups
(University of St Andrews, 2013)  ThesisThe 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
(University of St Andrews, 20130628)  ThesisIn 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
(University of St Andrews, 1986)  ThesisWe begin our study of amalgamations by examining some ideas which are wellknown for the category of Rmodules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in ... 
Generating "large" subgroups and subsemigroups
(University of St Andrews, 2016)  ThesisIn 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
(University of St Andrews, 2009)  ThesisWe 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
(University of St Andrews, 20160624)  ThesisIn this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FApresentable semigroups. We consider the properties of graph ... 
On defining groups efficiently without using inverses
(200207)  Journal articleLet 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 Dsimplicity of direct products, Byleen extensions, and other semigroup constructions
(University of St Andrews, 20151130)  ThesisIn 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
(University of St Andrews, 2018)  ThesisA group whose coword 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
(University of St Andrews, 2005)  ThesisThis 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
(University of St Andrews, 20190625)  ThesisComputational 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 ...