Non-isomorphism conjecture for generalized groups of the square and granny knots

Let $G_n(SK)$ and $G_n(GK)$ denote the generalized knot groups associated with the square knot $SK$ and granny knot $GK$, respectively, for integers $n\geq 2$. Non-isomorphism conjecture. The groups $G_n(SK)$ and $G_n(GK)$ are not isomorphic for each $n\geq 2$. The conjecture is motivated by the difference between their presentations, although computations of homomorphism counts and twisted Alexander polynomials have not distinguished the groups; their non-isomorphism remains open.