Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems

Download or read book Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems written by Denis V. Osin and published by American Mathematical Soc.. This book was released on 2006 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.