A family of links and the conway calculus

In 1969, J. H. Conway gave efficient methods of calculating abelian invariants of classical knots and links. The present paper includes a detailed exposition (with new proofs) of these methods and extensions in several directions. The main application given here is as follows. A link L of two unknotted components in S3 has the distinct lifting property for p if the lifts of each component to the /7-fold cover of S3 branched along the other are distinct. The /7-fold covers of these lifts are homeomorphic, and so L gives an example of two distinct knots with the same /7-fold cover. The above machinery is then used to construct an infinite family of links, each with the distinct lifting property for all p > 2.