A reduction theorem for the Feit conjecture

TL;DR

This paper proves that if all simple groups involved in a finite group satisfy a specific inductive condition, then Feit's conjecture holds for that group, potentially solving a long-standing problem in group theory.

Contribution

It establishes a reduction theorem linking the inductive Feit condition on simple groups to the validity of Feit's conjecture for all finite groups.

Findings

Proves the reduction theorem for Feit's conjecture

Connects local character features to the inductive Feit condition

Provides a pathway to solve Brauer's Problem 41

Abstract

We prove that if all the simple groups involved in a finite group $G$ satisfy the `inductive Feit condition', then Walter Feit's conjecture from 1980 holds for $G$. In particular, this would solve Brauer's Problem 41 from 1963 in the affirmative. This inductive Feit condition implies that some features of all the irreducible characters of finite groups can be found locally.