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May 10, 2026

On locally primitive bicirculants

Puntos clave

The research aims to classify finite vertex-transitive and locally primitive bicirculants, expanding on prior works in this area.
Utilized previous classifications and characterizations from earlier studies.
Completed the classification using combinatorial and graph theoretical techniques.
Achieved a complete classification of finite vertex-transitive bicirculants.
Identified key properties distinguishing locally primitive bicirculants from other forms.

Resumen

Abstract Finite arc‐transitive bicirculants with valency 3,4, or 5 have been classified in several previous papers. In 2022, Devillers, Giudici, and Jin gave a reductive characterization of finite arc‐transitive bicirculants, and using this, in 2023 Jin obtained a classification of finite 2‐arc‐transitive bicirculants. In this paper, we give a complete classification of finite vertex‐transitive and locally primitive bicirculants.

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