A reduction theorem for the Feit conjecture

2025/07/25 by Robert Boltje, Alexander Kleshchev, Boltje, Robert +5 · 2 citations
Mathematics · #20C15 (Primary) 20C25 #20C30 #20C33 #20D06 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Mathematics and Applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2507.19618

openalex publication_date 2025/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Feit's conjecture, the canonical Brauer induction formula, and Adams operations
• Inductive Feit and Galois-McKay conditions for some small-rank simple groups of Lie Type
• Towards the inductive McKay--Navarro Condition for groups of Lie type

Related

• Feit's conjecture, the canonical Brauer induction formula, and Adams operations
• A reduction theorem for the Character Triple Conjecture
• A counterexample for the conjecture of finite simple groups
• Inductive Feit and Galois-McKay conditions for some small-rank simple groups of Lie Type
• On Willems' conjecture on Brauer character degrees