GVZ-groups with two character degrees

Abstract

We investigate the finite groups $G$ for which $\ddot{I}‡(1{)}^2=|G:Z(\ddot{I}‡)|$ for all characters $\ddot{I}‡\in Irr(G)$ and $|cd(G)|=2$. We obtain some alternate characterizations of these groups and we obtain some information regarding the structure of these groups.