C. Roney‐Dougal

activity

20102026

most citedThe non-commuting, non-generating graph of a nilpotent group

9 citations · 43 across the 22 of their papers we have counts for

collaborators

24 papers

math.GR2026

Greedy bases and relational complexity of diagonal type groups

Hong Yi Huang, Colva M. Roney-Dougal

A base for a subgroup $G$ of $Sym (Ω)$ is a sequence of elements of $Ω$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b (G)$ . There is…

math.GR2025

On Cameron's Greedy Conjecture

Coen del Valle, Colva M. Roney-Dougal

A base for a permutation group $G$ acting on a set $Ω$ is a subset $B$ of $Ω$ whose pointwise stabiliser $G_{(B)}$ is trivial. There is a natural greedy algorit…

math.GR2025

Subgroups of symmetric groups: enumeration and asymptotic properties

Colva M. Roney-Dougal, Gareth Tracey

In this paper, we prove that the symmetric group $S_{n}$ has $2^{n^{2} /16 + o (n^{2})}$ subgroups, settling a conjecture of Pyber from 1993. We also derive asymptotically sharp upp…

math.GR2025

Irredundant bases for soluble groups

Sofia Brenner, Coen del Valle, Colva M. Roney-Dougal

Let $Δ$ be a finite set and $G$ be a subgroup of $Sym (Δ)$ . An irredundant base for $G$ is a sequence of points of $Δ$ yielding a strictly descending chain of pointwi…

math.CO2024

Regular bipartite multigraphs have many (but not too many) symmetries

Peter J. Cameron, Coen del Valle, Colva M. Roney-Dougal

Let $k$ and $l$ be integers, both at least 2. A $(k, l)$ -bipartite graph is an $l$ -regular bipartite multigraph with coloured bipartite sets of size $k$ . Define $χ (k, l)$ and $μ(k,l)…

math.GR2023

The relational complexity of linear groups acting on subspaces

Saul D. Freedman, Veronica Kelsey, Colva M. Roney-Dougal

The relational complexity of a subgroup $G$ of $Sym (Ω)$ is a measure of the way in which the orbits of $G$ on $Ω^{k}$ for various $k$ determine the original action of $G$ . V…

math.GR2023★ 1 cited

Irredundant bases for the symmetric group

Colva M. Roney-Dougal, Peiran Wu

An irredundant base of a group $G$ acting faithfully on a finite set $Γ$ is a sequence of points in $Γ$ that produces a strictly descending chain of pointwise stabiliser subgroups…

math.GR2023

The base size of the symmetric group acting on subsets

Coen del Valle, Colva M. Roney-Dougal

A base for a permutation group $G$ acting on a set $Ω$ is a subset $B$ of $Ω$ such that the pointwise stabiliser $G_{(B)}$ is trivial. Let $n$ and $r$ be positi…

math.GR2022★ 4 cited

Finite groups satisfying the independence property

Saul D. Freedman, Andrea Lucchini, Daniele Nemmi +1

We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$ , either ${x, y}$ is contained in a minimal generating…

math.GR2021★ 1 cited

Computing normalisers of intransitive groups

Mun See Chang, Christopher Jefferson, Colva M. Roney-Dougal

The normaliser problem takes as input subgroups $G$ and $H$ of the symmetric group $S_{n}$ , and asks one to compute $N_{G} (H)$ . The fastest known algorithm for this problem is simply e…

math.GR2021★ 8 cited

On relational complexity and base size of finite primitive groups

Veronica Kelsey, Colva M. Roney-Dougal

In this paper we show that if $G$ is a primitive subgroup of $S_{n}$ that is not large base, then any irredundant base for $G$ has size at most $5 lo g n$ . This is the first logari…

math.GR2021★ 1 cited

Primitive normalisers in quasipolynomial time

Mun See Chang, Colva M. Roney-Dougal

The normaliser problem has as input two subgroups $H$ and $K$ of the symmetric group $S_{n}$ , and asks for a generating set for $N_{K} (H)$ : it is not known to have a subexponential tim…

math.GR2021

Base sizes of primitive permutation groups

Mariapia Moscatiello, Colva M. Roney-Dougal

Let G be a permutation group, acting on a set Ωof size n. A subset B of Ωis a base for G if the pointwise stabilizer G_(B) is trivial. Let b(G) be the minimal size of a base for G.…

math.GR2020★ 9 cited

The non-commuting, non-generating graph of a nilpotent group

Peter J. Cameron, Saul D. Freedman, Colva M. Roney-Dougal

For a nilpotent group $G$ , let $Ξ (G)$ be the difference between the complement of the generating graph of $G$ and the commuting graph of $G$ , with vertices corresponding to central…

math.GR2020★ 1 cited

Maximal Cocliques in the Generating Graphs of the Alternating and Symmetric Groups

Veronica Kelsey, Colva M. Roney-Dougal

The generating graph $Γ (G)$ of a finite group $G$ has vertex set the non-identity elements of $G$ , with two elements connected exactly when they generate $G$ . A coclique in a graph…

math.GR2020★ 4 cited

Normalisers of primitive permutation groups in quasipolynomial time

Colva Roney-Dougal, Sergio Siccha

We show that given generators for subgroups $G$ and $H$ of $S_{n}$ , if $G$ is primitive then generators for $N_{H} (G)$ may be computed in quasipolynomial time, namely…

math.GR2019

Polynomial-time proofs that groups are hyperbolic

Derek Holt, Stephen Linton, Max Neunhoeffer +3

It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings, to define a new class of van Kam…

math.GR2018

Involution centralisers in finite unitary groups of odd characteristic

S. P. Glasby, Cheryl E. Praeger, Colva M. Roney-Dougal

We analyse the complexity of constructing involution centralisers in unitary groups over fields of odd order. In particular, we prove logarithmic bounds on the number of random ele…

math.GR2017★ 2 cited

On random presentations with fixed relator length

C. J. Ashcroft, Colva M. Roney-Dougal

The standard $(n, k, d)$ model of random groups is a model where the relators are chosen randomly from the set of cyclically reduced words of length $k$ on an $n$ -element generatin…

math.GR2016★ 6 cited

Generating sets of finite groups

Peter J. Cameron, Andrea Lucchini, Colva M. Roney-Dougal

We investigate the extent to which the exchange relation holds in finite groups $G$ . We define a new equivalence relation $\equiv_{m}$ , where two elements are equivalent i…

math.GR2015★ 4 cited

A note on the probability of generating alternating or symmetric groups

Luke Morgan, Colva M. Roney-Dougal

We improve on recent estimates for the probability of generating the alternating and symmetric groups $Alt (n)$ and $Sym (n)$ . In particular we find the sharp lower…

math.GR2014

Coprime invariable generation and minimal-exponent groups

Eloisa Detomi, Andrea Lucchini, Colva M. Roney-Dougal

A finite group $G$ is \emph{coprimely-invariably generated} if there exists a set of generators ${g_{1}, ..., g_{u}}$ of $G$ with the property that the orders $∣ g_{1} ∣, ..., ∣ g_{u} ∣$ are…

math.GR2014★ 1 cited

An explicit upper bound for the Helfgott delta in SL(2,p)

Jack Button, Colva Roney-Dougal

Helfgott proved that there exists a $δ > 0$ such that if $S$ is a symmetric generating subset of $S L (2, p)$ containing 1 then either $S^{3} = S L (2, p)$ or $∣ S^{3} ∣ \geq ∣ S ∣^{1 + δ}$ . It is know…

math.GR2010★ 1 cited

Constructive homomorphisms for classical groups

Scott H. Murray, Colva M. Roney-Dougal

Let Omega be a quasisimple classical group in its natural representation over a finite vector space V, and let Delta be its normaliser in the general linear group. We construct the…