Guarnieri–Vendramin conjecture for the number of braces of order p2qp^2q

For nZ+n\in\mathbb Z^+, let b(n)b(n) denote the number of isomorphism classes of finite left braces of order nn.

Guarnieri–Vendramin's conjecture. If pp and qq are primes such that p<qp<q and pq1p\nmid q-1, then

b(p2q)=4.b(p^2q)=4.

This is one of the brace-enumeration conjectures of Guarnieri and Vendramin. The supplied text identifies the conjecture but does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

Carsten Dietzel, “Braces of order p^2q”, arXiv:1801.06911 (2018).

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