A New Characterization of SimpleK3-Groups by Their Orders and Large Degrees of Their Irreducible Characters

It is a well-known fact that characters of a finite group can give important information of the structure of the group. Also it was proved by the second author that a finite simple group can uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite group by using less information of its character table, and successfully characterize K 3-groups by their orders and one or two irreducible character degrees of their character tables.