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The residual finiteness of HNN-extensions and generalized free products of nilpotent groups: a characterization

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

E. Raptis  and
D. Varsos
E. Raptis
Affiliation:
University of AthensPanepistemiopolis 15784 Athens, Greece
D. Varsos
Affiliation:
University of AthensPanepistemiopolis 15784 Athens, Greece
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Abstract

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We study the residual finiteness of free products with amalgamations and HNN-extensions of finitely generated nilpotent groups. We give a characterization in terms of certain conditions satisfied by the associated subgroups. In particular the residual finiteness of these groups implies the possibility of extending the isomorphism of the associated subgroups to an isomorphism of their isolated closures in suitable overgroups of the factors (or the base group in case of HNN-extensions).

MSC classification

Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E26: Residual properties and generalizations; residually finite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 408 - 420
Copyright
Copyright © Australian Mathematical Society 1992

References

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