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arXiv · 2305.03460

On a polynomial bound for the orbital diameter of primitive affine groups

Saveliy V. Skresanov
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Abstract

Let $ VG $ be a finite primitive affine permutation group, where $ V $ is a vector space of dimension $ d $ over the prime field $ \mathbb{F}_p $ and $ G $ is an irreducible linear group on $ V $. We prove that if $ p $ divides $ |G| $, then the diameters of all nondiagonal orbital graphs of $ VG $ are at most $ 9d^3 $. This improves an earlier exponential bound by A. Mar\'oti and the author.

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Saveliy V. Skresanov. 2023-05-05. On a polynomial bound for the orbital diameter of primitive affine groups. https://arxiv.org/abs/2305.03460

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