Doubly transitive groups and cyclic quandles

VENDRAMIN, LEANDRO

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN

MATH SOC JAPAN

Año: 2017 vol. 69 p. 1051 - 1057

0025-5645

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.