Abstract
We apply a construction of Rips to show that a number of algorithmic problems concerning certain small cancellation groups and, in particular, word hyperbolic groups, are recursively unsolvable. Given any integer k > 2, there is no algorithm to determine whether or not any small cancellation 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 subgroup of E is all of E, or is finitely presented, or has a finitely generated second integral homology group.
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