Isaacs-Navarro conjecture

The Isaacs-Navarro conjecture is a slight generalization of the McKay conjecture and is believed to hold for all finite groups.

Statement

Suppose $G$ is a finite group and $p$ is a prime number. Denote by $f(G,p,a)$ the number of equivalence classes of irreducible representations of $G$ over the complex numbers whose degree is congruent to $a$ or $-a$ modulo $p$. Then, if $a$ is not divisible by $p$, and $P$ is a $p$-Sylow subgroup of $G$, we have:

$\!f(G,p,a)=f(N_{G}(P),p,a)$

References

• New refinements of the McKay conjecture for finite groups by I. Martin Isaacs and Gabriel Navarro, Annals of Mathematics, Volume 156, Page 333 - 344(Year 2002): ^{ArXiV copyMore info}