DSpace Collection:
http://dspace1.isd.glam.ac.uk:80/dspace/handle/10265/347
2016-07-30T09:14:37ZPerfect commuting graphs
http://dspace1.isd.glam.ac.uk:80/dspace/handle/10265/826
Title: Perfect commuting graphs
Authors: Britnell, John; Gill, Nick
Abstract: We classify the finite quasisimple groups whose commuting graph
is perfect and we give a general structure theorem for finite groups whose
commuting graph is perfect.2016-01-01T00:00:00ZQuasirandom group actions
http://dspace1.isd.glam.ac.uk:80/dspace/handle/10265/825
Title: Quasirandom group actions
Authors: Gill, Nick
Abstract: Let G be a finite group acting transitively on a set Ω. We study what it means for this action to
be quasirandom, thereby generalizing Gowers’ study of quasirandomness in groups. We connect
this notion of quasirandomness to an upper bound for the convolution of functions associated with
the action of G on Ω. This convolution bound allows us to give sufficient conditions such that sets
S ⊆ G and ∆ 1 , ∆ 2 ⊆ Ω contain elements s ∈ S , ω 1 ∈ ∆ 1 , ω 2 ∈ ∆ 2 such that s(ω 1 ) = ω 2 . Other
consequences include an analogue of ‘the Gowers trick’ of Nikolov and Pyber for general group
actions, a sum-product type theorem for large subsets of a finite field, as well as applications to
expanders and to the study of the diameter and width of a finite simple group.
Description: 33 pages2016-01-01T00:00:00ZAbelian covers of alternating groups
http://dspace1.isd.glam.ac.uk:80/dspace/handle/10265/824
Title: Abelian covers of alternating groups
Authors: Barrantes, Daniel; Gill, Nick; Ramirez, Jeremias
Abstract: Let G = A_n , a finite alternating group. We study the commuting graph of G and establish,
for all possible values of n barring 13, 14, 17 and 19, whether or not the independence number is equal to
the clique-covering number.
Description: 11 pages2016-01-01T00:00:00ZPoiseuille flow of a smectic a liquid crystal
http://dspace1.isd.glam.ac.uk:80/dspace/handle/10265/730
Title: Poiseuille flow of a smectic a liquid crystal
Authors: Walker, Alan
Abstract: This article considers the dynamics of smectic A liquid crystals subjected to Poiseuille flow. Linearised governing equations are constructed using a recent dynamic theory for Smectic A [1]. These equations are solved analytically and the consequent solutions are then calculated for some typical experimental data in order to determine the explicit flow behaviour. Stability of flow and layer structure solutions are proved. Results show how the response time for small perturbations to the smectic layers depends upon the permeation constant and the layer compression modulus. [1] I.W. Stewart, Dynamic theory for smectic A liquid crystals, Continuum Mech. Thermodyn. 18 (2007) 343–360.2013-12-16T00:00:00Z