# On connected quandles of prime power order

## TL;DR

This paper classifies non-affine connected quandles of size p^3 for primes p > 3, using algebraic and group theory methods, and relates these structures to Bruck loops and automorphic loops.

## Contribution

It provides the first classification of non-affine connected quandles of size p^3 and links them to Bruck loops and automorphic loops, expanding understanding of algebraic structures of prime power order.

## Key findings

- Classified non-affine connected quandles of size p^3 for p > 3
- Established a correspondence between Bruck loops and automorphic loops of the same size
- Developed algebraic tools for studying connected quandles of prime power order

## Abstract

We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we obtain a classification of Bruck loops of the same size and that they are in one-to-one correspondence with commutative automorphic loops.