A236146 - OEIS

A236146

Number of primitive quandles of order n, up to isomorphism. A quandle is primitive if its inner automorphism groups acts primitively on it.

1, 0, 1, 1, 3, 0, 5, 2, 3, 1, 9, 0, 11, 1, 3, 15, 0, 17, 0, 1, 0, 21, 0, 10, 0, 8, 2, 27, 0, 29, 6, 0, 0, 0

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OFFSET

1,5

COMMENTS

Since a primitive quandle is connected, we have a(n) <= A181771(n) for all n.

Furthermore, since a primitive quandle is simple, we have a(n) <= A196111(n) for all n.

LINKS

James McCarron, Connected Quandles with Order Equal to Twice an Odd Prime, arXiv preprint arXiv:1210.2150 [math.GR], 2012.

Leandro Vendramin, Doubly transitive groups and cyclic quandles, arXiv:1401.4574 [math.GT], 2014-2017.

FORMULA

For odd primes p, a(p) = p - 2.

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

STATUS

approved