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Title 
A dichotomy for finitely generated subgroups of word hyperbolic groups 

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Published in  Topological and asymptotic aspects of group theory : AMS Special Session Probabilistic and Asymptotic Aspects of Group Theory, March 2627, 2004, Athens, Ohio : AMS Speical Session Topological Aspects of Group Theory, October 1617, 2004, Nashville, Tennessee. Athens, Ohio ; Nashville, Tennessee  2004  Providence, R.I.: American Mathematical society. 2006, p. 110  
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Contemporaray Mathematics; 394 

Abstract  Given L > 0 elements in a word hyperbolic group G, there exists a number M = M(G, L) > 0 such that at least one of the assertions is true: (i) these elements generate a free and quasiconvex subgroup of G; (ii) they are Nielsen equivalent to a system of L elements containing an element of length at most M up to conjugation in G. The constant M is given explicitly. The result is generalized to groups acting by isometries on Gromov hyperbolic spaces. For proof we use a graph method to represent finitely generated subgroups of a group.  
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Citation (ISO format)  ARZHANTSEVA, Goulnara N. A dichotomy for finitely generated subgroups of word hyperbolic groups. In: Topological and asymptotic aspects of group theory : AMS Special Session Probabilistic and Asymptotic Aspects of Group Theory, March 2627, 2004, Athens, Ohio : AMS Speical Session Topological Aspects of Group Theory, October 1617, 2004, Nashville, Tennessee. Athens, Ohio ; Nashville, Tennessee. Providence, R.I. : American Mathematical society, 2006. p. 110. (Contemporaray Mathematics; 394) https://archiveouverte.unige.ch/unige:12128 