Year: 2026
Type: preprint
Abstract: We prove a Hall $σ$-subgroup analogue of the McKay conjecture for $π$-separable groups proposed by G. Navarro. This result simultaneously generalizes the classical McKay conjecture and its $π$-separable version. More precisely, if $G$ is $π$-separable, $p$ is a prime and $σ=π\cup\{p\}$, then it is known that there exists $H$ a Hall $σ$-subgroup of $G$. In this case, we prove that $|{\rm Irr}_{σ'}(G)|=|{\rm Irr}_{σ'}(\mathbf{N}_{G}(H))|$.
Source: arXiv (Cornell University)
Author: Cabrera-Berenguer, David
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204533227
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