Gareth Tracey

activity

20152026

most citedOn the generalized Fitting height and insoluble length of finite groups

6 citations · 17 across the 17 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

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.

math.GR2020

An upper bound on the Chebotarev invariant of a finite group

Andrea Lucchini, Gareth Tracey

A subset ${g_{1}, \dots, g_{d}}$ of a finite group $G$ invariably generates $G$ if the set ${g_{1}^{x_{1}}, \dots, g_{d}^{x_{d}}}$ generates $G$ for every choice of $x_{i} \in G$ . The Che…

math.GR2020

Left $3$ -Engel elements in groups of exponent $60$

Gareth Tracey, Gunnar Traustason

Let $G$ be a group and let $x \in G$ be a left $3$ -Engel element of order dividing $60$ . Suppose furthermore that $⟨ x ⟩^{G}$ has no elements of order $8$ , $9$ and $25$ .…

math.GR2020★ 1 cited

On finite totally 2-closed groups

Alireza Abdollahi, Majid Arezoomand, Gareth Tracey

An abstract group $G$ is called totally $2$ -closed if $H = H^{(2), Ω}$ for any set $Ω$ with $G ≅ H \leq Sym (Ω)$ , where $H^{(2), Ω}$ is the largest subgroup of $Sym (Ω)$ who…

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

An upper bound on the Chebotarev invariant of a finite group

Left 3-Engel elements in groups of exponent 60

On finite totally 2-closed groups

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

Left $3$ -Engel elements in groups of exponent $60$