Work

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

Year: 2025

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2508.17664

Authors: Buturlakin, Alexander, Vasil'ev, Andrey V.

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences

OpenAlex ID: W7077880829

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