E. Pacifici

activity

20172023

most citedNon-solvable groups whose character degree graph has a cut-vertex. III

1 citations · 1 across the 4 of their papers we have counts for

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math.GR2023

Element orders and codegrees of characters in non-solvable groups

Z. Akhlaghi, E. Pacifici, L. Sanus

Given a finite group $G$ and an irreducible complex character $χ$ of $G$ , the codegree of $χ$ is defined as the integer $cod (χ) = ∣ G : ker χ ∣/ χ (1)$ . It was conjectured by G. Qian…

math.GR2022★ 1 cited

Non-solvable groups whose character degree graph has a cut-vertex. III

S. Dolfi, E. Pacifici, L. Sanus

Let $G$ be a finite group. Denoting by $cd (G)$ the set of the degrees of the irreducible complex characters of $G$ , we consider the {\it character degree graph} of $G$ : this…

math.GR2022

Conjugacy classes of maximal cyclic subgroups

M. Bianchi, R. D. Camina, Mark L. Lewis +1

In this paper, we set $η (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of $G$ . We consider $η$ and direct and semi-direct products. We characterize the norm…

math.GR2021

On Huppert's Rho-Sigma Conjecture

Zeinab Akhlaghi, Silvio Dolfi, Emanuele Pacifici

For an irreducible complex character $χ$ of the finite group $G$ , let $π (χ)$ denote the set of prime divisors of the degree $χ (1)$ of $χ$ . Denote then by $ρ (G)$ the union of all th…

math.GR2020

On solvable groups with one vanishing class size

Mariagrazia Bianchi, Rachel D. Camina, Mark L. Lewis +1

Let $G$ be a finite group, and let cs $(G)$ be the set of conjugacy class sizes of $G$ . Recalling that an element $g$ of $G$ is called a \emph{vanishing element} if there exists an…

math.GR2018

Bounding the number of vertices in the degree graph of a finite group

Zeinab Akhlaghi, Silvio Dolfi, Emanuele Pacifici +1

Let $G$ be a finite group, and let $cd (G)$ denote the set of degrees of the irreducible complex characters of $G$ . The degree graph $Δ (G)$ of $G$ is defined as the simple un…