## Kyoto Journal of Mathematics

### Extending properties to relatively hyperbolic groups

#### Abstract

Consider a finitely generated group $G$ that is relatively hyperbolic with respect to a family of subgroups $H_{1},\ldots,H_{n}$. We present an axiomatic approach to the problem of extending metric properties from the subgroups $H_{i}$ to the full group $G$. We use this to show that both (weak) finite decomposition complexity and straight finite decomposition complexity are extendable properties. We also discuss the equivalence of two notions of straight finite decomposition complexity.

#### Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 343-356.

Dates
Revised: 17 February 2017
Accepted: 22 February 2017
First available in Project Euclid: 18 January 2019

https://projecteuclid.org/euclid.kjm/1547802013

Digital Object Identifier
doi:10.1215/21562261-2018-0017

Mathematical Reviews number (MathSciNet)
MR3960296

Zentralblatt MATH identifier
07080107

#### Citation

Ramras, Daniel A.; Ramsey, Bobby W. Extending properties to relatively hyperbolic groups. Kyoto J. Math. 59 (2019), no. 2, 343--356. doi:10.1215/21562261-2018-0017. https://projecteuclid.org/euclid.kjm/1547802013

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