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Tameness and geodesic cores of subgroups

Part of: Low-dimensional topology Topological manifolds Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Rita Gitik
Rita Gitik
Affiliation:
A & H Consultants Ann Arbor, MI 48104 USA e-mail: ritagtk@math.lsa.umich.edu
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Abstract

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Let N be a finitely generated normal subgroup of a finitely generated group G. We show that if the trivial subgroup is tame in the factor group G/N, then N is that in G. We also give a short new proof of the fact that quasiconvex subgroups of negatively curved groups are tame. The proof utilizes the concept of the geodesic core of the subgroup and is related to the Dehn algorithm.

MSC classification

Secondary: 57M07: Topological methods in group theory 57M30: Wild knots and surfaces, etc., wild embeddings 57N10: Topology of general $3$-manifolds 20F34: Fundamental groups and their automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 2 , October 2000 , pp. 153 - 161
Copyright
Copyright © Australian Mathematical Society 2000

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