Character Triple Conjecture for $p$-Solvable Groups

TL;DR

This paper proves Sp"ath's Character Triple Conjecture for p-solvable groups, advancing the understanding of character theory in finite group representation, especially considering p-residues of characters.

Contribution

It provides a proof of Sp"ath's Character Triple Conjecture specifically for p-solvable groups, a key step in the broader context of Dade's Projective Conjecture.

Findings

Proof of Sp"ath's Character Triple Conjecture for p-solvable groups

Incorporation of p-residues of characters in the proof

Progress towards Dade's Projective Conjecture reduction

Abstract

In this paper, we prove Sp\"ath's Character Triple Conjecture for $p$-solvable groups. This is a conjecture proposed by Sp\"ath during the reduction process of Dade's Projective Conjecture to quasisimple groups. In addition, as suggested by Isaacs and Navarro, we take into account the $p$-residue of characters.