Andrea Lucchini

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20232026

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Showing 2023 · math.GRShow all

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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…