Some results on GVZ-groups with two character degrees

We investigate the finite groups G for which (1) ^2=|G: Z () | for all characters Irr (G) and |cd (G) |=2, where cd (G) =\ (1) | 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\.