A note on finite groups with few values in a column of the character table

Many structural properties of a finite group G are encoded in the set of irreducible character degrees of G. This is the set of (distinct) values appearing in the "first" column of the character table of G. In the current article, we study groups whose character table has a "non-first" column satisfying one particular condition. Namely, we describe groups having a nonidentity element on which all nonlinear characters take the same value.