4 problems

Levin conjecture. Every group equation over a torsion-free group $G$ is solvable over $G$.

Let $G=\operatorname{BS}(1,k)=\langle a,b\mid b^{-1}ab=a^k\rangle$ with $k>1$, equipped with the standard normal form described above, and let the solution language of an equation…

Let $\operatorname{BS}(1,k)=\langle a,b\mid b^{-1}ab=a^k\rangle$ with $k>1$, equipped with the standard normal form in which every element is uniquely expressible as … where…

Let $G$ be any group and let $w\in\mathbb F_n\ast G$, with $\varepsilon\colon\mathbb F_n\ast G\to\mathbb F_n$ the augmentation homomorphism sending $G$ to the neutral element. Gene…