On the generators of the kernels of hyperbolic group presentations

Abstract

In this paper we prove that if \(\mathcal{R}\) is a (not necessarily finite) set of words  satisfying certain small cancellation condition in a hyperbolic group \(G\) then the normal closure of \(\mathcal{R}\) is free. This result was first presented (for finite set \(\mathcal{R}\)) by T. Delzant [Delz] but the proof seems to require some additional argument. New applications of this theorem are provided.