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A solvability criterion for finite groups related to character degrees

Babak Miraali, Sajjad Mahmood Robati (2020)

Czechoslovak Mathematical Journal

Let m > 1 be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly m prime divisors. We show that such groups are solvable whenever m > 2 . Moreover, we prove that if G is a non-solvable group with this property, then m = 2 and G is an extension of A 7 or S 7 by a solvable group.

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