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 2018Show all

4 papers · 1 filter

math.GR2018

A left $3$ -Engel element whose normal closure is not nilpotent

Marialaura Noce, Gareth M. Tracey, Gunnar Traustason

We give an example of a locally nilpotent group $G$ containing a left $3$ -Engel element $x$ where $⟨ x ⟩^{G}$ is not nilpotent.

math.GR2018

Finite groups with large Chebotarev invariant

Andrea Lucchini, Gareth Tracey

A subset ${g_{1}, \dots, g_{d}}$ of a finite group $G$ is said to invariably generate $G$ if the set ${g_{1}^{x_{1}}, \dots, g_{d}^{x_{d}}}$ generates $G$ for every choice of $x_i \in G…

math.GR2018★ 1 cited

Generating maximal subgroups of finite almost simple groups

Andrea Lucchini, Claude Marion, Gareth Tracey

For a finite group $G$ , let $d (G)$ denote the minimal number of elements required to generate $G$ . In this paper, given a finite almost simple group $G$ and any maximal subgroup $H…

math.GR2018

Invariable generation of permutation and linear groups

Gareth M. Tracey

A subset $\left\{x_{1},x_{2},\hdots,x_{d}\right\}$ of a group $G$ \emph{invariably generates} $G$ if $\left\{x_{1}^{g_{1}},x_{2}^{g_{2}},\hdots,x_{d}^{g_{d}}\right\}$ generates $G$ …

A left 3-Engel element whose normal closure is not nilpotent

Finite groups with large Chebotarev invariant

Generating maximal subgroups of finite almost simple groups

Invariable generation of permutation and linear groups

A left $3$ -Engel element whose normal closure is not nilpotent