Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup

Fuente: arXiv
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Main Authors: Buturlakin, Alexander, Vasil'ev, Andrey V.
Format: Preprint
Published: 2025
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author Buturlakin, Alexander
Vasil'ev, Andrey V.
author_facet Buturlakin, Alexander
Vasil'ev, Andrey V.
contents Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in $\operatorname{Γ{L}}_1(q)$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_17664
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
Buturlakin, Alexander
Vasil'ev, Andrey V.
Group Theory
Combinatorics
20B05, 20B25, 05E30
Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in $\operatorname{Γ{L}}_1(q)$. 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.
title Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
topic Group Theory
Combinatorics
20B05, 20B25, 05E30
url https://arxiv.org/abs/2508.17664