On The Structure and Automorphism Group of Finite Alexander Quandles

TL;DR

This paper investigates the structure of finite Alexander quandles of prime order, demonstrating their high symmetry and the ability of automorphisms to map any pair of distinct elements to any other such pair.

Contribution

It proves that prime order Alexander quandles are generated by any two elements and that their automorphism groups are highly transitive on pairs of distinct elements.

Findings

Any pair of distinct elements generates the quandle.

Automorphisms can map any pair of distinct elements to any other such pair.

The automorphism group acts transitively on ordered pairs of distinct elements.

Abstract

We prove that an Alexander quandle of prime order is generated by any pair of distinct elements. Furthermore, we prove for such a quandle that any ordered pair of distinct elements can be sent to any other such pair by an automorphism of the quandle.