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A new characterization of simple \(K_3\)-groups by their orders and large degrees of their irreducible characters. (English) Zbl 1297.20012
Summary: 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 be 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.

MSC:
20C33 Representations of finite groups of Lie type
20C15 Ordinary representations and characters
20D06 Simple groups: alternating groups and groups of Lie type
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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