Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and $G/{\mathbf{O}}_{p^{\prime }}(G)$ has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.

中文翻译：

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主块中的字符程度

令G为一个有限群。我们证明，如果G的主p块中字符的度数集的大小最大为2，则G是p可解的，并且$G/{\mathbf{Ø}}_{p^{\prime }}（G）$有一个变态正态Sylow p-子群。证明以下问题的一般问题是：如果任意p块具有两个度数，则它们的缺陷组是亚贝尔贝叶式的仍然是开放的。