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On the Residual Finiteness of Polygonal Products of Nilpotent Groups

Published online by Cambridge University Press:  20 November 2018

Goansu Kim  and
C. Y. Tang
Goansu Kim
Affiliation:
Kangnung National University Kangnung, 210-702 Korea
C. Y. Tang
Affiliation:
University of Waterloo Waterloo, Ontario
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Abstract

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In general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.

Keywords

20E0620E2620F1820D4020F05Generalized free productspolygonal productsnilpotent groupsisolated subgroupssubgroup separability
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 3 , 01 September 1992 , pp. 390 - 399
Copyright
Copyright © Canadian Mathematical Society 1992

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