UNSOLVABLE PROBLEMS ABOUT SMALL CANCELLATION AND WORD HYPERBOLIC GROUPS

We apply a construction of Rips to show that a number of algorithmic p roblems concerning certain small cancellation groups and, in particula r, word hyperbolic groups, are recursively unsolvable. Given any integ er k > 2, them is no algorithm to determine whether or not any small c ancellation group can be generated by either two elements or more than k elements. There is a small cancellation group E such that there is no algorithm to determine whether or not any finitely generated subgro up of E is all of E, or is finitely presented, or has a finitely gener ated second integral homology group.