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Hyperbolic Groups are Hyperhopfian

Part of: Fiber spaces and bundles Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Robert J. Daverman
Robert J. Daverman
Affiliation:
Department of Mathematics University of TennesseeKnoxville, TN 37996-1300USA e-mail: daverman@novell.math.utk.edu
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Abstract

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The main result indicates that every finitely generated, residually finite, torsion-free, cohopfian group having on free Abelian subgroup of rank two is hyperhopfian. The argument relies on earlier work and ideas of Hirshon. As a corollary, fundamental groups of all closed hyperbolic manifolds are hyperhopfian.

Keywords

hyperhopfianhyper-cohopfianword hyperbolicfibrator

MSC classification

Secondary: 20E26: Residual properties and generalizations; residually finite groups 55R65: Generalizations of fiber spaces and bundles
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 126 - 130
Copyright
Copyright © Australian Mathematical Society 2000

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