4 problems

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

Let $G$ be the fundamental group of an aspherical two-complex, and let $\mathcal{P}=\langle G,x\mid R\rangle$ be a one-relator relative presentation whose natural homomorphism…

Let $l>0$ and $k>0$ with $l\neq k$, and let $\mathcal{Q}$ be the relative presentation considered in the paper. Define condition (AEJ-E) by the following alternatives: (i) $g=h^2$,…

Let $\mathcal{Q}$ be the relative presentation considered in the paper, with parameters $l>0$, $k\neq 0$ and non-trivial elements $g,h\in G$. Define … Say that Case $(P)$ holds whe…