Hall $\pi$-subgroups and characters of $\pi'$-degree

TL;DR

This paper explores the connection between Hall π-subgroups and irreducible characters of π'-degree in finite groups, extending previous results from a single odd prime to multiple odd primes.

Contribution

It generalizes Navarro and Tiep's result by analyzing the relationship for multiple odd primes instead of just one.

Findings

Extended the relationship to multiple odd primes.

Established new links between subgroup existence and character fields.

Generalized previous prime-specific results.

Abstract

We study the relationship between the existence of Hall $\pi$-subgroups and that of irreducible characters of $\pi'$-degree with prescribed fields of values in finite groups. This work extends a result of Navarro and Tiep from a single odd prime to multiple odd primes.