The enumeration of right Bol loops of order 3p3p up to isotopism

Let p>3p>3 be a prime, and consider right Bol loops of order 3p3p, with two such loops identified when they are isotopic. Enumeration claim. The number of right Bol loops of order 3p3p up to isotopism is

p+56+1.\left\lfloor \frac{p+5}{6}\right\rfloor+1.

This gives an explicit enumeration of these loops for every prime p>3p>3. The source provides no resolution evidence beyond the asserted statement.

Sources & referencesView supporting material

Primary source

Michael Kinyon, Gábor P. Nagy and Petr Vojtěchovský, “Bol loops and Bruck loops of order pq”, arXiv:1611.05785 (2017).

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