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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
Received: 2009-04-06
Revised: 2009-09-24
Published Online: 2010-03-10
Published in Print: 2009-October
© Heldermann Verlag
