Navarro's conjecture for coprime actions at all primes

Prove Navarro's conjecture that, whenever a finite group A acts coprimely by automorphisms on a finite group G and p is any prime, the number of A-invariant irreducible p-Brauer characters of G equals the number of irreducible p-Brauer characters of the fixed-point subgroup C_G(A).

Background

Navarro's conjecture is presented as a modular analogue of the Glauberman–Isaacs correspondence. It asserts equality between the A-fixed irreducible Brauer characters of G and the irreducible Brauer characters of C_G(A) under a coprime action. The paper proves the conjecture for primes p greater than 3, so the unrestricted formulation remains unresolved in the cases not covered by that theorem.

References

We use Theorem~(i) to investigate the following conjecture, proposed by Navarro, which is in some sense a modular analogue of the Glauberman--Isaacs correspondence. Suppose that $A$ and $G$ are finite groups such that $A$ acts coprimely via automorphisms on $G$. Let $p$ be a prime. Then |IBr_A(G)| = |IBr(C_G(A))|, where $IBr_A(G)$ denotes the set of irreducible $p$-Brauer characters of $G$ fixed by $A$.

— The Brauer $A(\infty)$ condition and Navarro's conjecture on Brauer characters under coprime actions  (2609.26441 - Feng et al., 22 Sep 2026) in Section 1, Introduction, Conjecture \ref{conj:coprime}