子群图包含一个大次顶点的有限群

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-04-04 DOI:10.1007/s00013-025-02121-1

Marius Tărnăuceanu

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引用次数: 0

摘要

Burness和Scott （J Aust Math Soc 87:329-357, 2009）对有限群G进行了分类，使得G的素阶子群的个数大于\(|G|/2-1\)。本文研究子群图中包含一个度大于\(|G|/2-1\)的顶点的有限群G。有限可解群的分类扩展了Burness和Scott的工作。

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Finite groups whose subgroup graph contains a vertex of large degree

Burness and Scott (J Aust Math Soc 87:329-357, 2009) classified finite groups G such that the number of prime order subgroups of G is greater than \(|G|/2-1\). In this note, we study finite groups G whose subgroup graph contains a vertex of degree greater than \(|G|/2-1\). The classification given for finite solvable groups extends the work of Burness and Scott.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.