Brauer characters and normal Sylow $p$-subgroups

TL;DR

This paper explores new criteria for the existence of normal Sylow p-subgroups in finite groups by analyzing variations of the Itô-Michler theorem through inequalities involving p-Brauer character degrees.

Contribution

It introduces novel criteria for normal Sylow p-subgroups based on inequalities related to p-Brauer character degrees, extending the Itô-Michler theorem.

Findings

New criteria for normal Sylow p-subgroups derived from p-Brauer character degrees.

Inequalities involving p-parts and p'-parts of p-Brauer character degrees.

Extensions of the Itô-Michler theorem to broader contexts.

Abstract

In this paper, we study some variations of the well-known It\^{o}-Michler theorem for $p$-Brauer characters using various inequalities involving the $p$-Brauer character degrees of finite groups. Several new criteria for the existence of a normal Sylow $p$-subgroup of finite groups are obtained using the $p$-parts and $p'$-parts of the $p$-Brauer character degrees.