4 problems

Let $L$ be a Bol magma with a neutral element, and let $\mathcal{J}(L)$ denote the set of elements of $L$ possessing a two-sided inverse. Non-closure conjecture. There exists a Bol…

Let $B(X)$ be a free Bol loop of exponent two. An automorphism of $B(X)$ is tame if it belongs to the group generated by the elementary automorphisms that, for a free generating se…

A free Bol loop of exponent two is a Bol loop freely generated in the variety of Bol loops satisfying $x^2=1$. Subloop freeness conjecture. Every subloop of a free Bol loop of expo…

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