---
tag: E9VNR66B01
kind: concept
name: Relatively hyperbolic group
aliases: [relatively-hyperbolic]
sources:
  - wikipedia: en:21993809@r1305298879
    locator: Relatively hyperbolic group
    note: adopted
    mention: wikipedia://en/21993809
    sections: [Summary]
same_as:
  wikidata: Q7310818
  wikipedia: Relatively hyperbolic group
inventory: [MEBY4802PP]
---

## 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.