11 problems

Let $L=(G,\circ)$ and $M=(G,*)$ be Moufang loops on the same set $G$ of order $n$, and define their distance by … Suppose that $L$ and $M$ have nonequivalent associators. Distance-…

Let $L=(G,\circ)$ and $M=(G,*)$ be Moufang $2$-loops on the same set $G$ of order $n$, and define their distance by … Quarter-distance isomorphism conjecture. If $d(\circ,*)<n^2/4$…

Let $n$ be the order of a Moufang loop, and let $\operatorname{Mlt}(L)$ denote its multiplication group. Polynomial-bound conjecture. The function … solves the problem of finding a…

Let $L$ be a nonassociative simple Moufang loop and let $H=\operatorname{Mlt}(L)_e$ be the stabilizer of the neutral element in the multiplication group of $L$. Simplicity conjectu…

Let $V \subset \mathbb{P}^3_L$ be a smooth cubic surface defined over a number field $L$. Let $\nu_1$ and $\nu_2$ be two different places of $L$. Suppose that there exists a non-as…

Globality conjecture. Every dual pair $(M,\mathcal{L})$ of Malcev algebras and their corresponding Moufang loops is global.

Sofic–Moufang conjecture. A group $G$ is sofic if and only if it is locally embeddable into finite Moufang loops.

Local embeddability conjecture. Every group is locally embeddable into finite Moufang loops.

Doro's conjecture. If $\operatorname{Nuc}(M)=1$, then $\operatorname{C}(M)$ is normal in $M$.

Let $L$ be a finite Moufang $p$-loop, where $p\ne 3$. Suppose $L$ is generated by a set $\{a_i\mid i\in I\}$ satisfying … for all $i,j,k\in I$, where $(x,y,z)$ denotes the associat…

Minimal identities conjecture. These identities form a minimal set of identities defining the variety ${\cal E}$.