Bounds for the Diameters of Orbital Graphs of Affine Groups

被引：3

作者：

Maroti, Attila ^{[1
]}

Skresanov, Saveliy V. ^{[2
]}

机构：

[1] Alfred Renyi Inst Math, Realtanoda utca 13-15, H-1053 Budapest, Hungary

[2] Sobolev Inst Math, 4 Acad Koptyug Ave, Novosibirsk, Russia

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2023年 / 51卷 / 03期

关键词：

Orbital graph; Diameter; Affine primitive permutation group; FINITE; THEOREM;

D O I：

10.1007/s10013-023-00607-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：617 / 631

页数：15

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