Luca Sabatini

collaborators

4 papers

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

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…

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

Probabilistic construction of some extremal $p$ -groups