Relatively hyperbolic group

Summary

In mathematics, relatively hyperbolic groups form an important class of groups of interest for geometric group theory. The main purpose in their study is to extend the theory of Gromov-hyperbolic groups to groups $G$ that may be regarded as hyperbolic assemblies of subgroups $H_i$, called peripheral subgroups, in a way that enables "hyperbolic reduction" of problems for $G$ to problems for the $H_i$s.