Luca Sabatini

activity

20232026

most citedOn stabilizers in finite permutation groups

1 citations · 1 across the 8 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.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…

Cayley graphs of quasirandom groups

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

Probabilistic construction of some extremal $p$ -groups