Degrees of $p$-rational characters and normality of Sylow $p$-subgroups

Silvio Dolfi; Pham Huu Tiep; Yu Zeng

Degrees of $p$-rational characters and normality of Sylow $p$-subgroups

Group Theory 2026-07-02 v1 Representation Theory

Authors: Silvio Dolfi , Pham Huu Tiep , Yu Zeng

Abstract

Several refinements of (the normality part of) the celebrated It\^o--Michler theorem were obtained during the last two decades, in which the condition of having $p'$ -degree, for a fixed prime $p$ , is imposed only on some subsets of complex irreducible characters of a finite group $G$ . We prove further extensions of these results, where this condition is now imposed on the irreducible characters which lie above the principal character of a Sylow $p$ -subgroup and are either $p$ -rational, or strongly real when $p=2$ .

Keywords

Itô-Michler theorem p-rational characters Sylow p-subgroups normality strongly real characters

Cite

@article{arxiv.2607.01706,
  title  = {Degrees of $p$-rational characters and normality of Sylow $p$-subgroups},
  author = {Silvio Dolfi and Pham Huu Tiep and Yu Zeng},
  journal= {arXiv preprint arXiv:2607.01706},
  year   = {2026}
}