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A dichotomy for finitely generated subgroups of word hyperbolic groups

Presented at Athens, Ohio ; Nashville, Tennessee, 2004
PublisherProvidence, R.I. : American Mathematical society
  • Contemporaray Mathematics; 394
Publication date2006

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.

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 26-27, 2004, Athens, Ohio : AMS Speical Session Topological Aspects of Group Theory, October 16-17, 2004, Nashville, Tennessee. Athens, Ohio ; Nashville, Tennessee. Providence, R.I. : American Mathematical society, 2006. p. 1–10. (Contemporaray Mathematics)
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