4-moves and the Dabkowski-Sahi invariant for knots

We study the 4-move invariant \crl\ for links in the 3-sphere developed by Dabkowski and Sahi, which is defined as a quotient of the fundamental group of the link complement. We develop techniques for computing this invariant and show that for several classes of knots it is equal to the invariant for the unknot; therefore, in these cases the invariant cannot detect a counterexample to the 4-move conjecture.