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arXiv · 2205.03593

Bounds for the diameters of orbital graphs of affine groups

Attila Maróti·Saveliy V. Skresanov
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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 \leq \mathrm{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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Attila Maróti, Saveliy V. Skresanov. 2022-05-07. Bounds for the diameters of orbital graphs of affine groups. https://arxiv.org/abs/2205.03593

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