  Given a knot K we may construct a group G_n(K) from the fundamental group of
K by adjoining an nth root of the meridian that commutes with the corresponding
longitude. These "generalised knot groups" were introduced independently by
Wada and Kelly, and contain the fundamental group as a subgroup. The square
knot SK and the granny knot GK are a well known example of a pair of distinct
knots with isomorphic fundamental groups. We show that G_n(SK) and G_n(GK) are
non-isomorphic for all n>1. This confirms a conjecture of Lin and Nelson, and
shows that the isomorphism type of G_n(K), n>1, carries more information about
K than the isomorphism type of the fundamental group. An appendix by David
Savitt contains some results on representations of the trefoil group in
PSL(2,p) that are needed for the proof.
