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Some simple groups which are determined by the set of their character degrees. I. (English) Zbl 0972.20006
Let $$G$$ be one of the finite simple groups $$L_2(2^f)$$ or $$Sz(2^f)$$. The author proves that every finite group whose set of degrees of the irreducible ordinary characters coincides with that of $$G$$ is isomorphic to the direct product of $$G$$ and an Abelian group. He also proposes the conjecture that the same holds for an arbitrary finite simple group $$G$$.

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