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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.

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
Full Text: DOI
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