Sum of the squares of the $p^{\prime }$-character degrees

Abstract

We study the sum of the squares of the irreducible character degrees not divisible by some prime $p$, and its relationship with the the corresponding quantity in a $p$-Sylow normalizer. This leads to study a recent conjecture by E. Giannelli, which we prove for $p=2$ and in some other cases.

Accepted in Pacific J. Math