仿射群轨道图直径的界。

IF 0.8 Q2 MATHEMATICS

Vietnam Journal of Mathematics Pub Date : 2023-01-01 Epub Date: 2023-02-10 DOI:10.1007/s10013-023-00607-5

Attila Maróti, Saveliy V Skresanov

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引用次数: 2

摘要

给出了有限仿射基置换群轨道图直径的一般界。例如，证明了具有非平凡点稳定器H≤GL（V）的有限仿射基元置换群的轨道直径，其中向量空间V在素域上具有维数d，可以仅根据d和log|V|/log|H|来有界。构造了几个具有大轨道直径的仿射基置换群的无穷大族。结果独立于有限单群的分类。

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Bounds for the Diameters of Orbital Graphs of Affine Groups.

General bounds are presented for the diameters of orbital graphs of finite affine primitive permutation groups. For example, it is proved that the orbital diameter of a finite affine primitive permutation group with a nontrivial point stabilizer H ≤GL(V ), where the vector space V has dimension d over the prime field, can be bounded in terms of d and $\log | V | / \log | H |$ only. Several infinite families of affine primitive permutation groups with large orbital diameter are constructed. The results are independent from the classification of finite simple groups.

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来源期刊

Vietnam Journal of Mathematics MATHEMATICS-

CiteScore

1.90

自引率

0.00%

发文量

期刊介绍： Vietnam Journal of Mathematics was originally founded in 1973 by the Vietnam Academy of Science and Technology and the Vietnam Mathematical Society. Published by Springer from 1997 to 2005 and since 2013, this quarterly journal is open to contributions from researchers from all over the world, where all submitted articles are peer-reviewed by experts worldwide. It aims to publish high-quality original research papers and review articles in all active areas of pure and applied mathematics.