3 problems

An equation $w(x)=1$ over a group $G$, where $w(x)\in G\ast\langle x\rangle_\infty$, is unimodular if the exponent sum of $x$ in $w(x)$ equals $\pm1$. It is solvable if there exist…

Let $\{w_j=1\}_{j\in J}$ be a system of equations with variables $\{x_i\}_{i\in I}$ over a group $G$. The system is non-singular when the rows of exponent sums of the variables in…

Kervaire–Laudenbach–Howie conjecture. Every independent system of equations over $G$ has a solution in an overgroup of $G$.