Andrea Lucchini

activity

20232026

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12 papers · 1 filter

math.GR2026

Bounded-orbit lattice representations of finite groups

JiaLi Du, Andrea Lucchini, Joy Morris +1

For a finite group $G$ , let $λ (G)$ denote the minimum number of orbits on the elements of a finite lattice $L$ with $Aut (L) ≅ G$ . Babai and Goodman conjectured th…

math.GR2026

Virtually generating graphs of pro- $p$ groups

Yiftach Barnea, Andrea Lucchini, Margherita Piccolo +1

We study the virtually generating graph of pro- $p$ groups. We show that various classes of pro- $p$ groups have connected virtually generating graph and we bound its diameter in the…

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

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…

math.GR2024

$p$ -elements in profinite groups

Andrea Lucchini, Nowras Otmen

We investigate some properties of the $p$ -elements of a profinite group $G$ . We prove that if $p$ is odd and the probability that a randomly chosen element of $G$ is a $p$ -element…

math.GR2023

Commuting probability for the Sylow subgroups of a finite group

Eloisa Detomi, Andrea Lucchini, Marta Morigi +1

For subsets $X, Y$ of a finite group $G$ , let $P r (X, Y)$ denote the probability that two random elements $x \in X$ and $y \in Y$ commute. Obviously, a finite group $G$ is nilpotent if…

math.GR2023

On the diameter of Engel graphs

Andrea Lucchini, Pablo Spiga

Given a finite group $G$ , the Engel graph of $G$ is a directed graph $Γ (G)$ encoding pairs of elements satisfying some Engel word. Namely, $Γ (G)$ is the directed graph, where the v…

math.GR2023

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…

Bounded-orbit lattice representations of finite groups

Virtually generating graphs of pro-p groups

Supersoluble groups and the probability of generating a supersoluble subgroup

Sectionally indecomposable groups

On the density of Sylow numbers

Profinite groups with many elements with large nilpotentizer and generalizations

Commutators between coprime order elements in non-abelian simple groups

The Chebotarev invariant for direct products of nonabelian finite simple groups

p-elements in profinite groups

Commuting probability for the Sylow subgroups of a finite group

On the diameter of Engel graphs

Solubilizers in profinite groups

Virtually generating graphs of pro- $p$ groups

$p$ -elements in profinite groups