E. Detomi

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20112025

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math.GR2022

Centralizers of commutators in finite groups

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Let $G$ be a finite group. A coprime commutator in $G$ is any element that can be written as a commutator $[x, y]$ for suitable $x, y \in G$ such that $π (x) \cap π (y) = \emptyset$ . Here $…

math.GR2022

The Engel graph of a finite group

Eloisa Detomi, Andrea Lucchini, Daniele Nemmi

For a finite group $G,$ we investigate the direct graph $Γ (G),$ whose vertices are the non-hypercentral elements of $G$ and where there is an edge $x \mapsto y$ if and only if $[x,_…