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The Residual Finiteness of Polygonal Products—Two Counterexamples

Published online by Cambridge University Press:  20 November 2018

R. B. J. T. Allenby
R. B. J. T. Allenby*
Affiliation:
School of Mathematics, University of Leeds Leeds, LS2 9JT England
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Abstract

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We show that, even under very favourable hypotheses, a polygonal product of finitely generated torsion free nilpotent groups amalgamating infinite cyclic subgroups is, in general, not residually finite, thus answering negatively a question of C. Y. Tang. A second example shows similar kinds of limitations apply even when the factors of the product are free abelian groups.

Keywords

Primary: 20E0620E2620F18secondary: 20F05generalised free productpolygonal productnilpotent groupabelian groupresidual finiteness
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 433 - 436
Copyright
Copyright © Canadian Mathematical Society 1994

References

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