Gareth Tracey

activity

20152021

most citedSharp upper bounds on the minimal number of elements required to generate a transitive permutation group

3 citations · 6 across the 5 of their papers we have counts for

collaborators

15 papers

math.GR2021★ 3 cited

Totally $2$ -closed finite groups with trivial Fitting subgroup

Majid Arezoomand, Mohammad A. Iranmanesh, Cheryl E. Praeger +1

A group $G$ is said to be totally $2$ -closed if in each of its faithful permutation representations, say on a set $Ω$ , $G$ is the largest subgroup of $Sym (Ω)$ which leaves…

math.GR2021

On the proportion of $p$ -elements in a finite group, and a modular Jordan type theorem

Gareth Tracey

In 1878, Jordan proved that if a finite group $G$ has a faithful representation of dimension $n$ over $C$ , then $G$ has a normal abelian subgroup with index bounded above…

math.GR2021

The transitive groups of degree 48 and some applications

Derek Holt, Gordon Royle, Gareth Tracey

The primary purpose of this paper is to report on the successful enumeration in Magma of representatives of the $195826352$ conjugacy classes of transitive subgroups of the sym…

math.GR2021★ 3 cited

Sharp upper bounds on the minimal number of elements required to generate a transitive permutation group

Gareth Tracey

The purpose of this paper is to prove that if $G$ is a transitive permutation group of degree $n \geq 2$ , then $G$ can be generated by $⌊ c n / lo g n ⌋$ elements, w…

math.GR2021

Some simplifications in the proof of the Sims conjecture

László Pyber, Gareth Tracey

We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.

math.GR2020

Locally finite $p$ -groups with a left 3-Engel element whose normal closure is not nilpotent

Anastasia Hadjievangelou, Marialaura Noce, Gunnar Traustason

For any odd prime $p$ , we give an example of a locally finite $p$ -group $G$ containing a left 3-Engel element $x$ where $⟨ x ⟩^{G}$ is not nilpotent.

Totally 2-closed finite groups with trivial Fitting subgroup

On the proportion of p-elements in a finite group, and a modular Jordan type theorem

The transitive groups of degree 48 and some applications

Sharp upper bounds on the minimal number of elements required to generate a transitive permutation group

Some simplifications in the proof of the Sims conjecture

Locally finite p-groups with a left 3-Engel element whose normal closure is not nilpotent

Totally $2$ -closed finite groups with trivial Fitting subgroup

On the proportion of $p$ -elements in a finite group, and a modular Jordan type theorem

Locally finite $p$ -groups with a left 3-Engel element whose normal closure is not nilpotent