vix.ing · top · new · best · stats · spec

Quasiprimitive groups with a biregular dihedral subgroup,and arc-transitive bidihedrants

2023/08/30 by Jiangmin Pan, Pan, Jiangmin, Fu‐Gang Yin +3
Engineering · Materials Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Quasicrystal Structures and Properties #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2308.15694

openalex publication_date 2023/08/30 · openalex created_date 2023/09/02 · openalex updated_date 2026/07/28

Abstract

A semiregular permutation group on a set \Ome is called \em bi-regular if it has two orbits. A classification is given of quasiprimitive permutation groups with a biregular dihedral subgroup. This is then used to characterize the family of arc-transitive graphs whose automorphism groups containing a bi-regular dihedral subgroup. We first show that every such graph is a normal r-cover of an arc-transitive graph whose automorphism group is either quasiprimitive or bi-quasiprimitive on its vertices, and then classify all such quasiprimitive or bi-quasiprimitive arc-transitive graphs.

Related