Connected Quandles with Order Equal to Twice an Odd Prime

Abstract

We show that there is an unique connected quandle of order twice an odd prime number greater than 3. It has order 10 and is isomorphic to the conjugacy class of transpositions in the symmetric group of degree 5. This establishes a conjecture of L. Vendramin.

Twenty-two pages. Preliminary version. v2: Corrected the definition of a simple quandle

References in corpus (2)

• Small connected quandles
• On The Structure and Automorphism Group of Finite Alexander Quandles

Cited by in corpus (3)

• Ring Theoretic Aspects of Quandles
• Doubly transitive groups and cyclic quandles
• Connected quandles of size $pq$ and $4p$