Irreducible p-constant characters of finite reflection groups

TL;DR

This paper classifies irreducible p-constant characters in finite reflection groups, nilpotent groups, and monomial groups, and discusses conjectures on the structure of groups with such characters.

Contribution

It provides a complete classification of p-constant characters for specific classes of finite groups and proposes new conjectures on their structural properties.

Findings

Classified p-constant characters for finite reflection groups

Extended classification to nilpotent and monomial groups

Proposed conjectures on group structures with p-constant characters

Abstract

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant characters for finite reflection groups, nilpotent groups and complete monomial groups. We also propose some conjectures about the structure of the groups admitting such characters.