极大类正常单项𝑝-groups的特征度

Pub Date : 2022-09-12 DOI:10.1515/jgth-2021-0212

Dongfang Yang, Heng Lv

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引用次数: 0

摘要

如果一个有限群𝐺的所有不可约性质均由其正规子群𝐺的线性性质导出，则该群为正规单项式群。本文研究了关于𝑝的极大类的正态单项𝑝-groups的最大不可约特征度和极大阿贝尔正规子群。特别地，我们确定了极大类的正常单项式5群的所有可能的不可约特征度集。

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Character degrees of normally monomial 𝑝-groups of maximal class

Abstract A finite group 𝐺 is normally monomial if all its irreducible characters are induced from linear characters of normal subgroups of 𝐺. In this paper, we study the largest irreducible character degree and the maximal abelian normal subgroup of normally monomial 𝑝-groups of maximal class in terms of 𝑝. In particular, we determine all possible irreducible character degree sets of normally monomial 5-groups of maximal class.

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