Luca Sabatini

collaborators

10 papers

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.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 $I^$ is a finite connected vertex-transitive cubic graph, then either $∣ V I^∣ \leq 90$ , or $I^$ is a split Praeger--Xu graph, or there exist two vertices $I^\pm$ and $Î…

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 SzabÃ³ (2013) by exhibiting a sequenc…

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

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…