Solvability and abelianness conjectures for finite superconnected quandles

A quandle is a binary algebraic structure; a finite quandle is superconnected when it has a Mal'cev term. A quandle is solvable in the sense of commutator theory, and it is abelian when it satisfies the corresponding abelianness condition.

Solvability and abelianness conjectures. (i) Every finite superconnected quandle is solvable. (ii) Every finite simple superconnected quandle is abelian.

These conjectures are motivated by the fact that finite latin quandles are solvable and their simple members are abelian. The paper's abstract states that it provides counterexamples to a conjecture suggested by computational data, so the status of the two parts should be checked against the paper's later results.