Andrea Lucchini

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math.GR2025

On the density of Sylow numbers

Andrea Lucchini, Pablo Spiga

Let $p$ be a prime number. We say that a positive integer $n$ is a Sylow $p$ -number if there exists a finite group having exactly $n$ Sylow $p$ -subgroups. When $p = 2$ , every odd int…

math.GR2025

Profinite groups with many elements with large nilpotentizer and generalizations

Martino Garonzi, Andrea Lucchini, Nowras Otmen

Given a profinite group $G$ and a family $F$ of finite groups closed under taking subgroups, direct products and quotients, denote by $F (G)$ the set of elements…

math.GR2025

Commutators between coprime order elements in non-abelian simple groups

Andrea Lucchini, Pablo Spiga

Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For…

math.GR2024

The Chebotarev invariant for direct products of nonabelian finite simple groups

Jessica Anzanello, Andrea Lucchini, Gareth Tracey

A subset ${g_{1}, \dots, g_{d}}$ of a finite group $G$ invariably generates $G$ if ${g_{1}^{x_{1}}, \dots, g_{d}^{x_{d}}}$ generates $G$ for every choice of $x_{i} \in G$ . The Chebotarev…