Nick Gill

activity

20062026

most citedGrowth in solvable subgroups of GL_r(Z/pZ)

24 citations · 93 across the 30 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

math.GR2020

Large minimal invariable generating sets in the finite symmetric groups

Daniele Garzoni, Nick Gill

For a finite group $G$ , let $m_{I} (G)$ denote the largest possible cardinality of a minimal invariable generating set of $G$ . We prove an upper and a lower bound for $m_{I} (S_{n})$ , whic…

math.GR2020★ 1 cited

On the number of conjugacy classes of a primitive permutation group with nonabelian socle

Daniele Garzoni, Nick Gill

Let $G$ be a primitive permutation group of degree $n$ with nonabelian socle, and let $k (G)$ be the number of conjugacy classes of $G$ . We prove that either $k (G) < n /2$ and $k(G)=o(…

math.GR2020

Nilpotent covers of symmetric and alternating groups

Nick Gill, Ngwava Arphaxad Kimeu, Ian Short

We prove that the symmetric group $S_{n}$ has a unique minimal cover $M$ by maximal nilpotent subgroups, and we obtain an explicit and easily computed formula for the order…

math.GR2020

On the height and relational complexity of a finite permutation group

Nick Gill, Bianca Lodá, Pablo Spiga

Let $G$ be a permutation group on a set $Ω$ of size $t$ . We say that $Λ \subseteq Ω$ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any…