Relatively hyperbolic group

A relatively hyperbolic group is a type of group in geometric group theory that generalizes the concept of hyperbolic groups. A group \( G \) is said to be relatively hyperbolic with respect to a collection of subgroups \( \mathcal{P} \) if the asymptotic geometry of \( G \) behaves somewhat like that of a hyperbolic group, but it can include additional structure provided by the subgroups in \( \mathcal{P} \).