Doubly transitive groups and cyclic quandles

Abstract

We prove that for n>2 there exists a quandle of cyclic type of size n if and only if n is a power of a prime number. This establishes a conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every finite quandle of cyclic type is an Alexander quandle. We also prove that finite doubly transitive quandles are of cyclic type. This establishes a conjecture of H. Tamaru.

6 pages. Final version

References in corpus (3)

• Quandle Colorings of Knots and Applications
• Two-point homogeneous quandles with prime cardinality
• On classification of quandles of cyclic type

Cited by in corpus (7)

• Ring Theoretic Aspects of Quandles
• Automorphism groups of quandles arising from groups
• A Survey of Racks and Quandles: Some recent developments
• Zero-divisors and idempotents in quandle rings
• On the Cycle Structure of Finite Racks and Quandles
• Homogeneous quandles arising from automorphisms of symmetric groups
• Flat connected finite quandles