Andrea Lucchini

activity

20242026

collaborators

6 papers

math.GR2026

Supersoluble groups and the probability of generating a supersoluble subgroup

Andrea Lucchini

Let $G$ be a finite group and let $P_{U} (G)$ denote the probability that two randomly chosen elements of $G$ generate a supersoluble subgroup. We prove that if $…

math.GR2026

Sectionally indecomposable groups

Andrea Lucchini, Nowras Otmen

We introduce the notion of sectional indecomposability and study it for finite groups: a group $H$ is sectionally indecomposable if, whenever $H$ is a section of a direct product $…

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

Solubilizers in profinite groups

Andrea Lucchini

The solubilizer of an element $x$ of a profinite group $G$ is the set of the elements $y$ of $G$ such that the subgroup of $G$ generated by $x$ and $y$ is prosoluble. We propose th…