Doubly transitive groups and cyclic quandles

Leandro Vendramin

doi:10.2969/jmsj/06931051

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arXiv · 1401.4574

Doubly transitive groups and cyclic quandles

Leandro Vendramin

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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.

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Leandro Vendramin. 2017-09-19. Doubly transitive groups and cyclic quandles. https://doi.org/10.2969/jmsj%2F06931051

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