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

2025/08/25 by Buturlakin, Alexander, Vasil'ev, Andrey V.
#05E30 #20B05 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.17664

Abstract

Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in \operatornameΓL₁(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.

Citations

• The automorphism groups of small affine rank 3 graphs
• A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers
• A classification of one dimensional affine rank three graphs
• Paley and the Paley graphs

Related

• On primitive 2-closed permutation groups of rank at most four
• Permutation groups and normal subgroups
• Commuting partial normal subgroups and regular localities
• Primitive permutation groups of finite Morley rank and affine type
• The automorphism groups of small affine rank 3 graphs