3 problems

Let $F$ be a free group, let $H\leq K\leq F$, and consider the morphism between their corresponding core graphs for every base. The extension is called algebraic when $H$ is not co…

Let $F$ be a free group, let $H\leq K\leq F$, and for each base of $F$ consider the morphism between the corresponding core graphs. Call the extension algebraic when $H$ is not con…

Rank-greater-than-two conjecture. The original Miasnikov–Ventura–Weil conjecture holds for $H\leq K\leq F_Y$ whenever $|Y|>2$.