2 problems

Let $G$ be a finitely generated soluble group, and let $Rat(G)$ denote the family of all rational subsets of $G$. Assume that $Rat(G)$ is a boolean algebra. Rational-subset conject…

Let $H$ and $G$ be groups, with $H$ nontrivial and $G$ not virtually free. The wreath-product undecidability conjecture. The rational subset membership problem for $H \wr G$ is und…