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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Metabelian Product of a Free Nilpotent Group with a Free Abelian Group

Margaret H. Dean
  • Dept. of Mathematics, Borough of Manhattan Community College of CUNY, 199 Chambers Street, New York, NY 10007, USA.
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Published Online: 2010-03-10 | DOI: https://doi.org/10.1515/GCC.2009.169

If two groups are residually-𝑃, their free product is not necessarily so; however, it is known that the free product of residually torsion-free nilpotent groups is again residually torsion-free nilpotent. In this paper it is shown that the free metabelian product of a free nilpotent group of class two with a free abelian group is residually torsion-free nilpotent.

Keywords:: Free product; free metabelian product; residually torsion-free nilpotent; metabelian groups

About the article

Received: 2009-04-06

Revised: 2009-09-24

Published Online: 2010-03-10

Published in Print: 2009-10-01

Citation Information: Groups – Complexity – Cryptology, Volume 1, Issue 2, Pages 169–180, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/GCC.2009.169.

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