Department of Mathematics and Statistics, McGill University, Montréal, P.Q., Canada H3A 2K6 ; Department of Mathematics, City College (CUNY), New York, New York 10031-9100
Abstract:
It is proved that the property of a group to be hyperbolic is preserved under HHN-extensions and amalgamated free products provided the associated (amalgamated) subgroups satisfy certain conditions. Some more general results about the preservation of hyperbolicity under graph products are also obtained. Using these results we describe the -completion is the field of rationals) of a torsion-free hyperbolic group as a union of an effective chain of hyperbolic subgroups, and solve the conjugacy problem in .