arXiv subjects

Gabriel A. L. Souza

Publications and source records attributed to Gabriel A. L. Souza.

3 recordsLinked to original sources

arXiv2026

Subnormalizers and character correspondences in $p$-solvable groups

A new family of local-global conjectures in the representation theory of finite groups has recently been proposed by Moretó. We show that one of the strongest of these conjectures, the strong subnormalizer conjecture, holds for $p$-solvable groups when $p$ is odd, under the condition that the subnormalizer subset is a subgroup. We also prove it in general when $p$ is odd and the $p$-length of the group is 1 and, in the process, obtain new properties related to the Glauberman correspondence.

math.RT↗

arXiv2025

Height zero characters and Galois automorphisms

Let $G$ be a finite group and let $p$ be a prime. In this paper, we prove a strengthened version of Brauer's height zero conjecture for the principal $p$-block of $G$ that takes the action of a certain group of Galois automorphisms into account. This answers a conjecture recently proposed by Malle, Moretó, Rizo and Schaeffer Fry. We then use this to obtain a structural result which can be seen as a Galois version of the Itô-Michler theorem.

math.RT↗

arXiv2025

On groups with at most five irrational conjugacy classes

Much work has been done to study groups with few rational conjugacy classes or few rational irreducible characters. In this paper we look at the opposite extreme. Let $G$ be a finite group. Given a conjugacy class $K$ of $G$, we say it is irrational if there is some $χ\in \operatorname{Irr}(G)$ such that $χ(K) \not \in \mathbb{Q}$. One of our main results shows that, when $G$ contains at most $5$ irrational conjugacy classes, then $|\operatorname{Irr}_{\mathbb{Q}}(G)| = |\operatorname{cl}_{\mathbb{Q}}(G)|$. This suggests some duality with the known results and open questions on groups with few rational irreducible characters. Our results are independent of the Classification of Finite Simple Groups.

math.GR↗