In 1993, Sim proved that all the faithful irreducible representations of a finite metacyclic group over any field of positive characteristic have the same degree. In this paper, we restrict our attention to non-modular representations and generalize this result for — (1) finite metabelian groups, over fields of positive characteristic coprime to the order of groups, and (2) finite groups having a cyclic quotient by an abelian normal subgroup, over number fields.

中文翻译：

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Metabelian 群的忠实不可约表示的程度

1993 年，Sim 证明了有限元环群在任何正特征域上的所有忠实不可约表示具有相同的度数。在本文中，我们将注意力限制在非模表示上，并将这一结果推广到——(1) 有限元贝尔群，在群阶的正特征互质域上，以及 (2) 具有循环商的有限群阿贝尔正态子群，在数域上。