Marco Vergani

collaborators

4 papers

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.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

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 $…