Luca Sabatini

activity

20232026

most citedOn stabilizers in finite permutation groups

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

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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…