4 problems

Rump's retraction conjecture. If $A$ is a quasilinear cycle set with $|A|>1$, then $A$ is retractable.

Let $b(n)$ denote the number of non-isomorphic left braces of size $n$. Let $p,q$ be prime numbers such that $p<q$ and $q\not\equiv1\bmod p$. The order-$p^2q$ counting conjecture.…

Let $b(n)$ denote the number of non-isomorphic left braces of size $n$, and let $p>3$ be a prime. The order-$9p$ counting conjecture. … The conjecture is suggested by the table of…

Let $b(n)$ denote the number of non-isomorphic left braces of size $n$. Let $p>3$ be a prime. The order-$4p$ counting conjecture. … The statement is presented as a conjecture sugge…