Luca Sabatini

activity

20232026

most citedOn stabilizers in finite permutation groups

1 citations · 2 across the 11 of their papers we have counts for

collaborators

11 papers

math.GR2026

Cayley graphs of quasirandom groups

Luca Sabatini

A finite group $G$ is $ε$ -quasirandom if all its nontrivial irreducible complex representations have degree at least $∣ G ∣^{ε}$ . Building on recent work of Golsefi…

math.CO2026

The base size of vertex-transitive cubic graphs

Marco Barbieri, Luca Sabatini, Pablo Spiga

We prove that if $Γ$ is a finite connected vertex-transitive cubic graph, then either $∣ V Γ∣ \leq 90$ , or $Γ$ is a split Praeger--Xu graph, or there exist two vertices $α$ and $β$ su…

math.GR2026

Expanding groups with large diameter

Sean Eberhard, Luca Sabatini

We study how the spectral gap and diameter of Cayley graphs depend strongly on the choice of generating set. We answer a question of Pyber and Szabó (2013) by exhibiting a sequence…

math.GR2026

On the maximal subgroups of almost simple and primitive perfect groups

Patricia Medina Capilla, Luca Sabatini

We prove that, if $G$ is a finite almost simple group and $H$ is a maximal subgroup of $G$ , then the $10$ th term of the derived series of $H$ is perfect. The same is true if $G$ is…

math.GR2025

Groups that produce expander graphs

Luca Sabatini

We survey the known group properties that a sequence of finite groups or group actions needs to satisfy to admit subsets of bounded cardinality producing expander Cayley or Schreie…

math.GR2025

Exponent and number of generators in a finite group

Luca Sabatini

We present a sharp upper bound for the number of generators of a finite group in terms of the ratio between the order and the exponent.

math.GR2025

Probabilistic construction of some extremal $p$ -groups

Sean Eberhard, Luca Sabatini

A $p$ -group $G$ is called *ab-maximal* if $∣ H : H^{'} ∣ < ∣ G : G^{'} ∣$ for every proper subgroup $H$ of $G$ . Similarly, $G$ is called * $d$ -maximal* if $d (H) < d (G)$ for every proper subgrou…

math.GR2024★ 1 cited

On stabilizers in finite permutation groups

Luca Sabatini

Let $G$ be a permutation group on the finite set $Ω$ . We prove various results about partitions of $Ω$ whose stabilizers have good properties. In particular, in every solvable perm…

math.CO2024

The diameter of random Schreier graphs

Daniele Dona, Luca Sabatini

We give a combinatorial proof of the following theorem. Let $G$ be any finite group acting transitively on a set of cardinality $n$ . If $S \subseteq G$ is a random set of size $k$ ,…

math.GR2024

Quasirandom and quasisimple groups

Marco Barbieri, Luca Sabatini

Fix $ε > 0$ . We say that a finite group $G$ is $ε$ -quasirandom if every nontrivial irreducible complex representation of $G$ has degree at least $|G|^\varepsilo…

math.GR2023★ 1 cited

On finite $d$ -maximal groups

Andrea Lucchini, Luca Sabatini, Mima Stanojkovski

Let $d$ be a positive integer. A finite group is called $d$ -maximal if it can be generated by precisely $d$ elements, while its proper subgroups have smaller generating sets. For $…

Cayley graphs of quasirandom groups

The base size of vertex-transitive cubic graphs

Expanding groups with large diameter

On the maximal subgroups of almost simple and primitive perfect groups

Groups that produce expander graphs

Exponent and number of generators in a finite group

Probabilistic construction of some extremal p-groups

On stabilizers in finite permutation groups

The diameter of random Schreier graphs

Quasirandom and quasisimple groups

On finite d-maximal groups

Probabilistic construction of some extremal $p$ -groups

On finite $d$ -maximal groups