Year: 2026
Type: article
Abstract: Very recently, the first and third authors proposed a new conjecture on characters of finite groups, related to the McKay conjecture. Let p be a prime number and G a finite group. We say that a p -element $$x \in G$$ x ∈ G is picky in G if it is contained in a unique Sylow p -subgroup of G . The simplest formulation of this conjecture predicts the existence of a bijection between the set of irreducible characters of G that do not vanish on a picky p -element x , and the corresponding set of irreducible characters of the normalizer of the unique Sylow p -subgroup of G containing x . Moreover, this bijection is expected to satisfy several natural conditions. For example, the p -parts of the degrees of corresponding characters should coincide, and their values at x should also be suitably related. In this paper, we prove this conjecture for p -solvable groups when p is odd.
Source: Mathematische Zeitschrift
Authors: Alexander Moretó, Gabriel Navarro, Noelia Rizo
Institution: Universitat de València
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7140772113