E. Pacifici

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20242026

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math.GR2026

The Gruenberg-Kegel graph of finite solvable groups that are character-quadratic or semi-rational

Irene Crispi, Sara C. DebÃ³n, Emanuele Pacifici +2

A finite group $G$ is said to be semi-rational if the set of generators of each cyclic subgroup of $G$ is contained in at most two $G$ -conjugacy classes. This is equivalent to the…

math.GR2026

Groups with a conjugacy class that is the difference of two normal subgroups

Mark L. Lewis, Lucia Morotti, Emanuele Pacifici +2

We consider finite groups having a conjugacy class that is the difference of two normal subgroups. That is, suppose $G$ is a group and $M$ and $N$ are normal subgroups so that $N <…

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…