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

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