Classification of simple quandles of small order

TL;DR

This paper introduces quasiprimitive quandles, characterizes them using permutation groups, and enumerates all finite non-affine simple quandles up to order 4096, advancing the classification of algebraic structures.

Contribution

It defines quasiprimitive quandles and provides a comprehensive enumeration of finite non-affine simple quandles up to order 4096, a novel classification achievement.

Findings

Defined quasiprimitive quandles using permutation groups

Enumerated non-affine simple quandles up to order 4096

Connected algebraic structures with permutation group analysis

Abstract

In this article, we define quasiprimitive quandles and describe them with the help of quasiprimitive permutation groups. As a consequence, we enumerate finite non-affine simple quandles up to order $4096$.