On classification of quandles of cyclic type

TL;DR

This paper classifies quandles of cyclic type by describing their isomorphism classes using cyclic permutations, providing a complete classification for sizes up to 12.

Contribution

It offers a new description of quandles of cyclic type via cyclic permutations and classifies all such quandles up to size 12.

Findings

Complete classification of quandles of cyclic type up to size 12

Description of isomorphism classes using cyclic permutations

Identification of the structure of quandles of cyclic type

Abstract

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic type with cardinality up to $12$.