Geodesic
On the generators of the kernels of hyperbolic group presentations
Algebra and discrete mathematics, Tome 11 (2011) no. 2, pp. 18-50

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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.
Keywords: hyperbolic groups, small cancellation. 
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     author = {Vladimir Chaynikov},
     title = {On the generators of the kernels of hyperbolic group presentations},
     journal = {Algebra and discrete mathematics},
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     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_11_2_a1/}
}
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Vladimir Chaynikov. On the generators of the kernels of hyperbolic group presentations. Algebra and discrete mathematics, Tome 11 (2011) no. 2, pp. 18-50. http://geodesic.mathdoc.fr/item/ADM_2011_11_2_a1/