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 A7 or S7 by a solvable group.

中文翻译：

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与字符度相关的有限群的可解性判据

让 m > 1 是一个固定的正整数。在本文中，我们考虑有限群，每个群的非线性特征度恰好有 m 个素因数。我们证明，当 m > 2 时，此类群是可解的。此外，我们证明，如果 G 是具有此性质的不可解群，则 m = 2 并且 G 是 A7 或 S7 的可解群的扩展。