Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915888314187776 |
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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 |
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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 |