#### Geometry & Topology Monographs 1 (1998),
The Epstein Birthday Schrift,
paper no. 4, pages 99-116.

## Controlled embeddings into groups that have no non-trivial finite quotients

### Martin R Bridson

**Abstract**.
If a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index.

Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space Overline(X) such that Overline(X) has no non-trivial finite-sheeted coverings.
**Keywords**.
Finite quotients, embeddings, non-positive curvature

**AMS subject classification**.
Primary: 20E26, 20E06, 53C70. Secondary: 20F32, 20F06.

**E-print:** `arXiv:math.GR/9810188`

Submitted: 16 November 1997.
Published: 25 October 1998.

Notes on file formats
Martin R Bridson

Mathematical Institute, 24--29 St Giles', Oxford, OX1 3LB

Email: bridson@maths.ox.ac.uk

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