具有单个伽罗瓦共轭类的有限群的刻划

Pub Date : 2023-07-25 DOI:10.1515/jgth-2022-0215

Yuedi Zeng, Dongfang Yang

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引用次数: 0

摘要

摘要设𝐺是一个有限群，设Irr s²(G) \ maththrm {Irr}_{\mathfrak{s}}(G)是𝐺的不可约复字符的集合，使得χ²(1)2 \chi(1)^{2}不能除其核的索引。本文对Irr s²(G) \mathr {Irr}_{\ mathfrk {s}}(G)中任意两个字符为伽罗瓦共轭的有限群𝐺进行了分类。特别地，我们证明了这样的群是可解的，拟合高度为2。

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A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters

Abstract Let 𝐺 be a finite group and let Irr s ⁢ ( G ) \mathrm{Irr}_{\mathfrak{s}}(G) be the set of irreducible complex characters 𝜒 of 𝐺 such that χ ⁢ ( 1 ) 2 \chi(1)^{2} does not divide the index of the kernel of 𝜒. In this paper, we classify the finite groups 𝐺 for which any two characters in Irr s ⁢ ( G ) \mathrm{Irr}_{\mathfrak{s}}(G) are Galois conjugate. In particular, we show that such groups are solvable with Fitting height 2.

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