Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
Group Theory
2026-03-26 v3 Combinatorics
Abstract
Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in . This brings us to a description of the relatively closed subgroups of permutation groups with a cyclic regular normal subgroup. Our results, in particular, provide a classification of the minimal nontrivial one-dimensional affine association schemes which generalizes the recent Muzychuk classification of the one-dimensional affine rank 3 graphs.
Cite
@article{arxiv.2508.17664,
title = {Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup},
author = {Alexander Buturlakin and Andrey V. Vasil'ev},
journal= {arXiv preprint arXiv:2508.17664},
year = {2026}
}