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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
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