The SQ-universality and residual properties of relatively hyperbolic groups

By Goulnara Arzhantseva, Ashot Minasyan, Denis V. Osin. 2006

73 citations recorded by the source corpus.

In this paper we study residual properties of relatively hyperbolic groups. In particular, we show that if a group G is non-elementary and hyperbolic relative to a collection of proper subgroups, then G is SQ-universal.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d0890e0cb5f9e37cdf5f4f92bdd350e2025373bd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Franccois Dahmani
2. Vincent Guirardel
3. Denis V. Osin
4. P. Caprace
5. Carolyn R. Abbott
6. Nicolas Monod
7. Gilbert Levitt

In Discrete Mathematics and Combinatorics

1. Michael Hull
2. Denis V. Osin
3. Carolyn R. Abbott
4. Franccois Dahmani
5. Vincent Guirardel
6. S. Balasubramanya
7. Alessandro Sisto
8. P. Caprace

In Geometry and Topology

1. Denis V. Osin
2. Vincent Guirardel
3. Michael Hull
4. Franccois Dahmani
5. Alessandro Sisto
6. P. Caprace
7. Carolyn R. Abbott
8. S. Balasubramanya

Citations in the corpus

• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “Many of the ideas used here are due to Olshanskii [101] and Minasyan [93] (see also [9]).”
• Isometry groups of non‐positively curved spaces: discrete subgroups (2009, background): “Indeed, a lattice in a simple Lie group of rank one is relatively hyperbolic (see [40] or [70]) and as such has numerous infinitely generated normal subgroups (and is even SQ-universal; see [47] or [33] for the hyperbolic case and [3] for the general relative case).”
• Small cancellation in acylindrically hyperbolic groups (2013, background): “ith two conjugacy classes; this was the rst known example of any nitely generated group with two conjugacy classes other than Z=2Z. Other applications of Osin’s version of Theorem 1.1 can be found in [1, 3, 4, 16, 23, 32]. The goal of this paper is to prove a version of Theorem 1.1 for a larger clas”
• Small cancellations over relatively hyperbolic groups and embedding theorems (2004, methodology): “Further applications of our methods can be found in [2], [1], [4], [19], [20], [25].”
• Hyperbolic structures on groups (2017, background): “, and the latter poset is much easier to understand. Yet another application is obtained by combining Theorem2.7with a \relatively hyperbolic" version of the SQ-universality of F 2 (see [54] and [5]). Corollary 2.8. Let Gbe an acylindrically hyperbolic group and let Hbe a nitely generated group”
• Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “For a survey of SQ-universality we refer to [4,81].”