Some results on GVZ-groups with two character degrees

We investigate the finite groups G for which χ(1)²=|G:Z(χ)| for all characters χ ∈ Irr(G) and $|cd(G)|=2$, where cd(G)=\χ(1)| χ ∈ Irr(G)\. We call such a group a GVZ-group with two character degrees. We establish bijections between the sets of characters of some groups obtained from a GVZ-group with two character degrees. Additionally we obtain some alternate characterizations of a GVZ-group with two character degrees and we construct a GVZ-group having the character degree set \1,p\.