C. Monetta

activity

20172025

most citedA criterion for metanilpotency of a finite group

11 citations · 37 across the 10 of their papers we have counts for

collaborators

11 papers

math.GR2025

On finite groups with soluble centralisers

Valentina Grazian, Carmine Monetta, Gareth Tracey

We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element cen…

math.GR2023★ 3 cited

Group nilpotency from a graph point of view

Valentina Grazian, Andrea Lucchini, Carmine Monetta

Let $Γ_{G}$ denote a graph associated with a group $G$ . A compelling question about finite groups asks whether or not a finite group $H$ must be nilpotent provided $Γ_{H}$ is isomorphi…

math.GR2023★ 4 cited

A conjecture related to the nilpotency of groups with isomorphic non-commuting graphs

Valentina Grazian, Carmine Monetta

In this work we discuss whether the non-commuting graph of a finite group can determine its nilpotency. More precisely, Abdollahi, Akbari and Maimani conjectured that if $G$ and $H…

math.GR2022

On the structure of finite groups determined by the arithmetic and geometric means of element orders

Valentina Grazian, Carmine Monetta, Marialaura Noce

In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions stron…

math.GR2021★ 3 cited

$p$ -nilpotency criteria for some verbal subgroups

Yerko Contreras Rojas, Valentina Grazian, Carmine Monetta

Let $G$ be a finite group, let $p$ be a prime and let $w$ be a group-word. We say that $G$ satisfies $P (w, p)$ if the prime $p$ divides the order of $x y$ for every $w$ -value $x$ in…

math.GR2021★ 2 cited

On some series of a group related to the non-abelian tensor square of groups

Raimundo Bastos, Ricardo de Oliveira, Carmine Monetta +1

Let $G$ be a group. We denote by $ν (G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$ . In this paper we prove that the derived subgroup $ν (G)^{'}$ …

math.GR2020★ 2 cited

The exponent of the non-abelian tensor square and related constructions of $p$ -groups

R. Bastos, E. de Melo, N. Gonçalves +1

Let $G$ be a finite $p$ -group. In this paper we obtain bounds for the exponent of the non-abelian tensor square $G \otimes G$ and of $ν (G)$ , which is a certain extension of $G \oti…

math.GR2019

Boundedly finite conjugacy classes of tensors

Raimundo Bastos, Carmine Monetta

Let $n$ be a positive integer and let $G$ be a group. We denote by $ν (G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$ . Set $T_{\otimes}(G) =…

math.GR2018★ 6 cited

A nilpotency criterion for some verbal subgroups

Carmine Monetta, Antonio Tortora

The word $w = [x_{i_{1}}, x_{i_{2}}, \dots, x_{i_{k}}]$ is a simple commutator word if $k \geq 2, i_{1} \neq = i_{2}$ and $i_{j} \in {1, \dots, m}$ , for some $m > 1$ . For a finite group $G$ , we prove that…

math.GR2018★ 6 cited

Coprime commutators in finite groups

Carmine Monetta, Raimundo Bastos

Let $G$ be a finite group and let $k \geq 2$ . We prove that the coprime subgroup $γ_{k}^{*} (G)$ is nilpotent if and only if $∣ x y ∣ = ∣ x ∣∣ y ∣$ for any $γ_{k}^{*}$ -commutators $x, y \in G$ of cop…

math.GR2017★ 11 cited

A criterion for metanilpotency of a finite group

Raimundo Bastos, Carmine Monetta, Pavel Shumyatsky

We prove that the $k$ th term of the lower central series of a finite group $G$ is nilpotent if and only if $∣ ab ∣ = ∣ a ∣∣ b ∣$ for any $γ_{k}$ -commutators $a, b \in G$ of coprime orders.