## Tokyo Journal of Mathematics

- Tokyo J. Math.
- Volume 42, Number 1 (2019), 83-112.

### On Relative Hyperbolicity for a Group and Relative Quasiconvexity for a Subgroup

Yoshifumi MATSUDA, Shin-ichi OGUNI, and Saeko YAMAGATA

#### Abstract

We consider two families of subgroups of a group. Assume that each subgroup which belongs to one family is contained in some subgroup which belongs to the other family. We then discuss relations of relative hyperbolicity for the group with respect to the two families, respectively. If the group is hyperbolic relative to the two families, respectively, then we consider relations of relative quasiconvexity for a subgroup of the group with respect to the two families, respectively.

#### Article information

**Source**

Tokyo J. Math., Volume 42, Number 1 (2019), 83-112.

**Dates**

First available in Project Euclid: 18 July 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.tjm/1563436915

**Mathematical Reviews number (MathSciNet)**

MR3982051

**Zentralblatt MATH identifier**

07114902

**Subjects**

Primary: 20F67: Hyperbolic groups and nonpositively curved groups

Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

#### Citation

MATSUDA, Yoshifumi; OGUNI, Shin-ichi; YAMAGATA, Saeko. On Relative Hyperbolicity for a Group and Relative Quasiconvexity for a Subgroup. Tokyo J. Math. 42 (2019), no. 1, 83--112. https://projecteuclid.org/euclid.tjm/1563436915