E. Detomi

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20112022

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16 papers · 1 filter

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,_…

math.GR2021

Strong conciseness of coprime and anti-coprime commutators

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

A coprime commutator in a profinite group $G$ is an element of the form $[x, y]$ , where $x$ and $y$ have coprime order and an anti-coprime commutator is a commutator $[x, y]$ such th…

math.GR2021

On the rank of a verbal subgroup of a finite group

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

We show that if $w$ is a multilinear commutator word and $G$ a finite group in which every metanilpotent subgroup generated by $w$ -values is of rank at most $r$ , then the rank of t…

math.GR2021

On the commuting probability for subgroups of a finite group

Eloisa Detomi, Pavel Shumyatsky

Let $K$ be a subgroup of a finite group $G$ . The probability that an element of $G$ commutes with an element of $K$ is denoted by $P r (K, G)$ . Assume that $P r (K, G) \geq ε$ for some fix…

math.GR2020

Profinite groups in which the probabilistic zeta function has no negative coefficients

Eloisa Detomi, Andrea Lucchini

To a finitely generated profinite group $G$ , a formal Dirichlet series $P_{G} (s) = \sum_{n \in N} a_{n} (G) / n^{s}$ is associated, where $a_{n} (G) = \sum_{∣ G : H ∣ = n} μ (H, G)$ and $μ(H,G…