Andrea Lucchini

activity

20242026

collaborators

6 papers

math.CO2026

On the finite group whose proper enhanced power graph is claw-free

Sudip Bera, Andrea Lucchini

Let $G$ be a finite group. The \emph{enhanced power graph} of $G$ , denoted by $E (G)$ , is the graph with vertex set $G$ in which two vertices $u$ and $v$ are adjacent if a…

math.GR2026

2-covering numbers of some finite solvable groups

Andrea Lucchini

A 2-covering for a finite group $G$ is a set of proper subgroups of $G$ such that every pair of elements of $G$ is contained in at least one subgroup in the set. The minimal number…

math.GR2025

Finite groups with the minimal generating set exchange property

Andrea Lucchini, Patricia Medina Capilla

Let $d (G)$ be the smallest cardinality of a generating set of a finite group $G .$ We give a complete classification of the finite groups with the property that, whenever $ \langle…

math.GR2024

On finite groups whose power graph is claw-free

Pallabi Manna, Santanu Mandal, Andrea Lucchini

A graph is called claw-free if it contains no induced subgraph isomorphic to the complete bipartite graph $K_{1, 3}$ . The undirected power graph of a group $G$ has vertices the ele…

math.GR2024

On the connectivity of the generating and rank graphs of finite groups

Andrea Lucchini, Daniele Nemmi

The generating graph encodes how generating pairs are spread among the elements of a group. For more than ten years it has been conjectured that this graph is connected for every f…

math.GR2024

Abelian supplements in almost simple groups

Mauro Costantini, Andrea Lucchini, Daniele Nemmi

Let $G$ be a finite almost simple group with socle $G_{0}$ . In this paper we prove that whenever $G / G_{0}$ is abelian, then there exists an abelian subgroup $A$ of $G$ such that $G=AG_…