Hello,

i am very interested in knot theory, especially in knot groups and knot polynomials. Therefore i am reading the book of Crowell and Fox (Introduction to knot theory). I want to compute some Alexanderpolynomials (with the technique they use in this book, thus Fox calculu, Abelization, free groups etc.) I can do this for special knots for example trefoil and cinquefoil (this are also exercises in this book). But now i want to compute the Alexanderpolynomial of the torus knot $T_{p,q}$ for $p$ and $q$ coprime. Therefore they want to prove that the following formula holds: $$\Delta(T_{p,q})=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$$ if the knot group is $G(T_{p,q})= \langle x,y:x^p=y^q\rangle$ (this is not so difficult to prove). But here i can give the solution (or the way to solve it -.-). I have also make computations but they they are not good. Can someone help me with this? Thank you for help :)