Irreducible characters taking root of unity values on p-singular elements

TL;DR

This paper investigates the properties of irreducible characters in finite p-solvable groups that take roots of unity values specifically on p-singular elements, revealing new structural insights.

Contribution

It introduces a detailed analysis of irreducible characters with roots of unity values on p-singular elements in finite p-solvable groups, a novel focus in character theory.

Findings

Character values are roots of unity on p-singular elements.

Structural properties of p-solvable groups are elucidated.

New classifications of irreducible characters are proposed.

Abstract

In this paper we study finite p-solvable groups having irreducible complex characters chi in Irr(G) which take roots of unity values on the p-singular elements of G.