Bounds for the Diameters of Orbital Graphs of Affine Groups

Attila Maróti; Saveliy V Skresanov

doi:10.1007/s10013-023-00607-5

Bounds for the Diameters of Orbital Graphs of Affine Groups

Vietnam J Math. 2023;51(3):617-631. doi: 10.1007/s10013-023-00607-5. Epub 2023 Feb 10.

Authors

Attila Maróti¹, Saveliy V Skresanov²

Affiliations

¹ Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, 1053 Budapest, Hungary.
² Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, Russia.

Abstract

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.

Keywords: Affine primitive permutation group; Diameter; Orbital graph.