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On the distance between the axes of elliptic elements generating a free product of cyclic groups

On the distance between the axes of elliptic elements generating a free product of cyclic groups Abstract Let f and g be elliptic Möbius transformations of respective orders m ≥3, n ≥2, and let s , φ be the hyperbolic distance and angle between their axes. In this paper we prove that for the group 〈 f , g 〉 is discrete, nonelementary and isomorphic to the free product of cyclic groups. Several examples are given showing the effectiveness of the above estimate for cosh s . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

On the distance between the axes of elliptic elements generating a free product of cyclic groups

Rasskazov, Alexey
Advances in Geometry , Volume 6 (1) – Jan 26, 2006
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Publisher
de Gruyter
Copyright
Copyright © 2006 by the
ISSN
1615-715X
eISSN
1615-7168
DOI
10.1515/ADVGEOM.2006.006
Publisher site
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Abstract

Abstract Let f and g be elliptic Möbius transformations of respective orders m ≥3, n ≥2, and let s , φ be the hyperbolic distance and angle between their axes. In this paper we prove that for the group 〈 f , g 〉 is discrete, nonelementary and isomorphic to the free product of cyclic groups. Several examples are given showing the effectiveness of the above estimate for cosh s .

Journal

Advances in Geometry – de Gruyter

Published: Jan 26, 2006

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