Luca Sabatini

activity

20242026

most citedFixing two points in primitive solvable groups

2 citations · 3 across the 4 of their papers we have counts for

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math.GR2026

Arithmetic properties of solubilizers

Luca Sabatini

Let $G$ be a finite group and $x \in G$ . In 2013, Hai-Reuven proved that the cardinality of the centralizer of $x$ divides the cardinality of the solubilizer of $x$ . Settling a con…

math.GR2026

Sylow synchronization in finite groups: the good case

Hong Yi Huang, Francesca Lisi, Aluna Rizzoli +1

Let $G$ be a finite solvable group such that, for any prime $p$ and any quotient $Q$ of $G$ , there are two Sylow $p$ -subgroups of $Q$ intersecting in $O_{p} (Q)$ . Then, for every fami…

math.GR2026

Diameter bounds for arbitrary finite groups and applications

Sean Eberhard, Elena Maini, Luca Sabatini +1

We prove a strong general-purpose bound for the diameter of a finite group depending only on the diameters of its composition factors and the maximal exponent of a normal abelian s…