5 problems

Let $m\geq 3$, and let $q(4m)$ denote the number of braces $B$ whose multiplicative group $(B,\circ)$ is a generalised quaternion group of order $4m$. Guarnieri–Vendramin's conject…

Let ${\mathcal G}=({\mathcal V},{\mathcal E})$ be a brace, meaning a bipartite matching covered graph with no nontrivial tight cuts. An edge $e$ of ${\mathcal G}$ is thin if, for e…

Strong nilpotence conjecture for the Wedderburn radical. The Wedderburn radical of $A$ should be strongly nilpotent.

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

Ault–Watters' conjecture. Every nilpotent group of class $2$ is the adjoint group of a radical ring of nilpotency class $3$.