We consider groups where the centers of the irreducible characters form a chain. We obtain two alternate characterizations of these groups, and we obtain some information regarding the structure of these groups. Using our results, we are able to classify those groups where the kernels of the irreducible characters form a chain. We show that a result of Nenciu regarding nested GVZ groups is really a result about nested groups. We obtain an alternate proof of a theorem of Isaacs regarding the existence of p -groups with a given set of irreducible character degrees.

中文翻译：

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不可约字符的中心形成链的组

我们考虑不可约字符的中心形成链的组。我们获得了这些群体的两个替代特征，并获得了有关这些群体结构的一些信息。使用我们的结果，我们能够对那些不可约字符的核形成链的组进行分类。我们表明，Nenciu 关于嵌套 GVZ 组的结果实际上是关于嵌套组的结果。我们获得了关于具有给定不可约特征度集的 p 群存在的艾萨克定理的替代证明。