Author:
Maróti Attila,Skresanov Saveliy V.
Abstract
AbstractGeneral 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 $\log |V|/\log |H|$
log
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V
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/
log
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H
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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.
Funder
European Research Council
Hungarian Scientific Research Fund
RAS Fundamental Research Program
ELKH Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
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