字符和Sylow子群别列化

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-01-22 DOI:10.1016/j.jalgebra.2024.12.031

Eugenio Giannelli , Noelia Rizo , A.A. Schaeffer Fry , Carolina Vallejo

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引用次数: 0

摘要

我们根据G的主3块中高度为零的字符的个数，刻画了有限群G何时拥有一个9阶阿贝尔化的Sylow 3-子群P，从而解决了Navarro， Sambale和Tiep在2018年提出的一个猜想。在此过程中，我们证明了Laradji最近关于块中高度为零的字符位于某些正常子群的给定字符之上的数量的结果是成立的，而没有任何关于最大缺陷块的组的假设。

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Characters and Sylow subgroup abelianization

We characterize when a finite group G possesses a Sylow 3-subgroup P with abelianization of order 9 in terms of the number of height zero characters lying in the principal 3-block of G, settling a conjecture put forward by Navarro, Sambale, and Tiep in 2018. Along the way, we show that a recent result by Laradji on the number of character of height zero in a block that lie above a given character of some normal subgroup holds, without any hypothesis on the group for blocks of maximal defect.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.