Multivariate Alexander quandles, II. The involutory medial quandle of a link

Joyce showed that for a classical knot K, the order of the involutory medial quandle is vertical bar det K vertical bar. Generalizing Joyce's result, we show that for a classical link L of mu >= 1 components, the order of the involutory medial quandle is mu vertical bar det L vertical bar/2(mu-1). In particular, IMQ(L) is infinite if and only if det L = 0. We also relate IMQ(L) to several other link invariants.