Luca Sabatini

activity

20202022

2

in finite groups

4 citations · 12 across the 8 of their papers we have counts for

collaborators

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5 papers · 1 filter

math.GR2021★ 4 cited

Nilpotent subgroups of class $2$ in finite groups

Luca Sabatini

We show that every finite group $G$ of size at least $3$ has a nilpotent subgroup of class at most $2$ and size at least $∣ G ∣^{1/32 l o g l o g ∣ G ∣}$ . This answers a question of Pyber,…

math.GR2021★ 1 cited

Abelian sections of the symmetric groups with respect to their index

Luca Sabatini

We show the existence of an absolute constant $α > 0$ such that, for every $k \geq 3$ , $G := Sym (k)$ , and for every $H ⩽ G$ of index at least $3$ , one has $|H…

math.GR2021

On finite groups with polynomial diameter

Luca Sabatini

Given a finite group $G$ and a generating set $S \subseteq G$ , the diameter $d iam (G, S)$ is the least integer $n$ such that every element of $G$ is the product of at most $n$ elemen…

math.GR2021★ 2 cited

The growth of abelian sections

Luca Sabatini

Given an abstract group $G$ , we study the function $a b_{n} (G) := sup_{∣ G : H ∣ \leq n} ∣ H / [H, H] ∣$ . If $G$ has no abelian composition factors, then $a b_{n} (G)$ is bounded by a polynomial:…

math.CO2021★ 3 cited

Random Schreier graphs and expanders

Luca Sabatini

Let the group $G$ act transitively on the finite set $Ω$ , and let $S \subseteq G$ be closed under taking inverses. The Schreier graph $S c h (G ↺ Ω, S)$ is the graph wit…

Nilpotent subgroups of class 2 in finite groups

Abelian sections of the symmetric groups with respect to their index

On finite groups with polynomial diameter

The growth of abelian sections

Random Schreier graphs and expanders

Nilpotent subgroups of class $2$ in finite groups