E. Pacifici

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20242026

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5 papers · 1 filter

math.GR2025

The N-prime graph and the Subgroup Isomorphism Problem

Emanuele Pacifici, Angel del Rio, Marco Vergani

We introduce a directed graph related to a group $G$ , which we call the N-prime graph $I^_{N} (G)$ of $G$ and which is a refinement of the classical Gruenberg-Kegel graph. The…

math.GR2025

On Camina pairs and the Fitting subgroup

Mark L. Lewis, Emanuele Pacifici

In this paper, we consider the relationship between the Fitting subgroup and the Camina kernel of a Camina pair.

math.GR2025

Groups with conjugacy classes of coprime sizes

Rachel D. Camina, Attila MarÃ³ti, Emanuele Pacifici +6

Suppose that $x$ , $y$ are elements of a finite group $G$ lying in conjugacy classes of coprime sizes. We prove that $⟨ x^{G} ⟩ \cap ⟨ y^{G} ⟩$ is an abelian nor…

math.GR2025

Group cosets with all elements of equal order

Alan R. Camina, Rachel D. Camina, Mark L. Lewis +3

Let $G$ be a finite group and $N$ a proper, nontrivial, normal subgroup of $G$ . If, for every element $x$ of $G$ not lying in $N$ , the elements in the coset $x N$ all have the same…

math.GR2025

On quadratic rational Frobenius groups

Emanuele Pacifici, Marco Vergani

Let $G$ be a finite group and, for a given complex character $I ¨ $ of $G$ , let $Q (I ¨ )$ denote the field extension of $Q$ obtained by adjoining all the values $…