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On the modular version of Ito’s theorem on character degrees for groups of odd order. (English) Zbl 0611.20004

The following result is proved: Let \(\pi\) be a set of primes, and let p be a prime not contained in \(\pi\). Let G be a finite group of odd order, and suppose that, for all irreducible p-modular characters \(\beta\) of G, \(\beta\) (1) is not divisible by primes in \(\pi\). Then the \(\pi\)-length of G is at most 2.
Reviewer: B.Külshammer

MSC:

20C20 Modular representations and characters
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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