6 problems

Special half-isomorphism conjecture. Every half-isomorphism between automorphic loops is special.

Let $G$ be a uniquely 2-divisible group, and let $(G,\circ)$ be the commutative loop arising from the construction in which $G$ is equipped with the operation $\circ$. A group is m…

Let $p$ be a prime, let $M_2(\mathbb F_p)$ denote the $2\times 2$ matrices over $\mathbb F_p$, and let $Q_{\mathbb F_p}(A)$ be the loop associated with a matrix…

Bruck–Paige conjecture. Every diassociative automorphic loop is Moufang.

Conjecture on the isomorphism classes. There are precisely three isomorphism classes of such automorphic loops.

Classification conjecture. The loops $Q(A)$ and $Q(B)$ are isomorphic if and only if $A$ and $B$ are of the same type.