Wed, 10 May 95 11:26:55 BST The Kim-Kostrikin group has 4 generators a, b, c, d, and is defined by the relations ada = cb, bdb = ac, cdc = ba, abc = 1. It is one of a 2-parameter family of fundamental groups of 3-manifolds and all the others are known to be infinite. Calculations using the Aachen system SPAS suggest that it also is infinite, but that's not a proof. Dave Johnson