Classifying Camina groups: A theorem of Dark and Scoppola

Abstract

Recall that a group $G$ is a Camina group if every nonlinear irreducible character of $G$ vanishes on $G \setminus G^{\p}$. Dark and Scoppola classified the Camina groups that can occur. We present a different proof of this classification using Theorem~2, which strengthens a result of Isaacs on Camina pairs. Theorem~2 is of independent interest.