caa a22 4500 445862610 CHVBK 20180317145448.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00031-011-9134-9 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9134-9 Glutsyuk Alexey Laboratoire J.-V.Poncelet, UMI 2615 du CNRS et l'Université Indépendante de Moscou, Moscow, Russia aut Instability of nondiscrete free subgroups in lie groups [Elektronische Daten] [Alexey Glutsyuk] We study finitely-generated nondiscrete free subgroups in Lie groups. We address the following question first raised by Étienne Ghys: is it always possible to make arbitrarily small perturbations of the generators of the free subgroup in such a way that the new group formed by the perturbed generators be not free? In other words, is it possible to approximate generators of a free subgroup by elements satisfying a nontrivial relation? We prove that the answer to Ghys' question is positive and generalize this result to certain nonfree subgroups. We also consider the question on the best approximation rate in terms of the minimal length of relation in the approximating group. We give an upper bound on the optimal approximation rate as $$ {e^{ - c{l^\kappa }}} $$, where c > 0 is a constant, l the minimal length of relation and 0.19 < κ < 0.2. Springer Science+Business Media, LLC, 2011 Transformation Groups SP Birkhäuser Verlag Boston 16/2(2011-06-01), 413-479 1083-4362 16:2<413 2011 16 31 https://doi.org/10.1007/s00031-011-9134-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9134-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Glutsyuk Alexey Laboratoire J.-V.Poncelet, UMI 2615 du CNRS et l'Université Indépendante de Moscou, Moscow, Russia aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/2(2011-06-01), 413-479 1083-4362 16:2<413 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer