Browsing by Subject "Mathematics"
Now showing items 1-20 of 72
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2-Uniform covering groups of elementary Abelian 2-Group
(NUI Galway, 2023-04-24)A covering group of an elementary abelian group of order p(n) is a group G of order pn+(n 2 ) consisting of the following data: • G has generators x1, . . . , xn. • The commutator subgroup of G is equal to the centre ... -
An algorithm for the unit group of the Burnside ring of a finite group
(Cambridge University Press, 2007-01)In this note we present an algorithm for the construction of the unit group of the Burnside ring Ω(G) of a finite group G from a list of representatives of the conjugacy classes of subgroups of G. -
Algorithms for Nilpotent Linear Groups
(2011-03-04)In this thesis, we develop practical algorithms for irreducibility and primitivity testing of finite nilpotent linear groups defined over various fields of characteristic zero, including number fields and rational function ... -
Algorithms for the accurate and efficient solution of fourth order boundary-layer problems
(NUI Galway, 2022-06-10)In this thesis, we study the analysis and numerical solution of second-order complex-valued reactiondiffusion equations, and two families of fourth-order singularly perturbed problems. The problems are all singularly ... -
Automorphisms of Pairwise Combinatorial Designs
(2012-02-14)In this thesis, we investigate group actions on certain families of pairwise combinatorial designs, in particular Hadamard matrices and symmetric 2-(4t-1, 2t-1, t-1) designs. A Hadamard matrix H is called cocyclic if a ... -
Behavioural fluency: An investigation of instructional approaches to build fluency with academic skills and associated outcomes
(2014-07-11)This thesis investigates the efficacy of instructional approaches designed to build fluency with mathematics skills, specifically, frequency-building, Precision Teaching (PT) and the Morningside Mathematics Fluency curricula. ... -
The BMR freeness conjecture for the 2-reflection groups
(American Mathematical Society, 2016-10-12)We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections. -
Cell complexes database for the Bianchi groups
(NUI Galway, 2016-05-18)This is a database of quotients by Bianchi groups of two-dimensional cellular equivariant retracts of Hyperbolic three-space. The Bianchi groups SL(2, A), with A the ring of integers in the imaginary quadratic number field ... -
Characterising bases of pure difference ideals
(NUI Galway, 2020-09-10)In this thesis, we study the basis sets of pure difference ideals, that is, ideals that are generated by differences of monic monomials. We examine the action of the hyperoctahedral group on the defining ideal of the Segre ... -
Classification Problems for Finite Linear Groups
(2013-03-08)This thesis is concerned with classification problems for finite linear groups. Our main concern is with groups of prime degree, and groups defined over finite fields and fields of zero characteristic. We use the computational ... -
Cohomology of Coxeter arrangements and Solomon's descent algebra
(American Mathematical Society, 2014-06-19)We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and ... -
Completions of partial matrices
(2015-03-23)A partial matrix over a field is a matrix whose entries are either elements of the field or independent indeterminates. A completion of a partial matrix is any matrix that results from assigning a field element to each ... -
Computation of cohomology operations for finite groups
(NUI Galway, 2018-08-31)The main result of this dissertation is the computation of all Steenrod squares on the Mod 2 cohomology of all groups of order dividing 32 and all but 58 groups of order 64; partial information on Steenrod square is ... -
Computational homology of n-types
(2014-01-10)An n-type X is a CW-space with homotopy groups \pi_iX=0 for all i>n. Up to homotopy equivalence such a space can be specified algebraically by means of a simplicial group whose Moore complex is trivial in degrees >= n. For ... -
Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six
(Elsevier, 2013-01-08)In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its Orlik-Solomon algebra as a sum of characters induced from ... -
Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
(Elsevier, 2014-11-06)In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the p-th graded ... -
Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four
(Elsevier, 2012-06-03)In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced ... -
Computing the table of marks of a cyclic extension
(American Mathematical Society, 2012-02-24)The subgroup pattern of a finite group C is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we present an algorithm for the computation of the ... -
Dihedral codes
(2009)In this thesis we give new constructions of a number of extremal type II codes. Algebraic proofs are provided that the constructions do in fact yield the codes. The codes are constructed using group rings of which the ...