Character Values of $p$-solvable groups on picky elements

TL;DR

This paper proves a new character-theoretic conjecture related to the McKay conjecture for p-solvable groups when p is odd, advancing understanding of group characters.

Contribution

It establishes the conjecture for p-solvable groups with odd p, providing a significant step forward in character theory and group representation.

Findings

Proved the conjecture for p-solvable groups with odd p.

Enhanced understanding of character values on picky elements.

Connected the conjecture to the broader McKay conjecture framework.

Abstract

A new conjecture on characters of finite groups, related to the McKay conjecture, was proposed recently by the first and third authors. In this paper, we prove it for $p$-solvable groups when $p$ is odd.