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

Martin R Bridson

Geometry & Topology Monographs 1 (1998) 99–116

DOI: 10.2140/gtm.1998.1.99

arXiv: math.GR/9810188

Abstract

If a class of finitely generated groups G is closed under isometric amalgamations along free subgroups, then every G ∈G can be quasi-isometrically embedded in a group G ∈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 X such that X has no non-trivial finite-sheeted coverings.

Keywords

finite quotients, embeddings, non-positive curvature

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Publication

Received: 16 November 1997
Published: 21 October 1998

Authors
Martin R Bridson
Mathematical Institute
24–29 St Giles'
Oxford
OX1 3LB