Work

The McKay conjecture with group automorphisms and the Okuyama-Wajima argument

Year: 2025

Type: article

Abstract: Let N be normal subgroup of a finite group G , p be a prime, P be a Sylow p -subgroup of G and θ be a P -invariant irreducible character of N . Suppose that G / N is a p -solvable group. In this note we show that, whenever a finite group A acts on G stabilizing P , there exists an A -equivariant McKay bijection between irreducible characters lying over θ of degree prime to p of G and N G ( P ) N . This is a consequence of a recent result of D. Rossi. Our approach here is independent from Rossi's and follows the original idea of the proof of the McKay conjecture for p -solvable groups. In particular, we rely on the so-called Okuyama-Wajima argument to deal with characters above Glauberman correspondents. For this purpose, we generalize a classical result of P. X. Gallagher on the number of irreducible characters of G lying over θ .

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2025.108155

Authors: Adele Maltempo, Carolina Vallejo

Institutions: University of Birmingham, University of Florence

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni