具有2个生成的Sylow子组及其字符表的组

IF 0.7 3区数学 Q2 MATHEMATICS

Pacific Journal of Mathematics Pub Date : 2022-05-26 DOI:10.2140/pjm.2023.323.337

Alexander Moret'o, Benjamin Sambale

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引用次数: 0

摘要

设G是一个有Sylow P -子群P的有限群，我们证明了G的特征表决定了P是否有极大幂零类和P是否为极小非阿贝尔群。后一种结果是根据其组成因子对相应组G进行精确分类得到的。对于P约束群G，我们进一步证明了字符表决定了P是否可以由两个元素生成。

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Groups with 2-generated Sylow subgroups and their character tables

Let G be a finite group with Sylow p-subgroup P. We show that the character table of G determines whether P has maximal nilpotency class and whether P is a minimal non-abelian group. The latter result is obtained from a precise classification of the corresponding groups G in terms of their composition factors. For p-constrained groups G we prove further that the character table determines whether P can be generated by two elements.

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来源期刊

Pacific Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.