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ON RESIDUAL FINITENESS OF GRAPHS OF NILPOTENT GROUPS

E. RAPTIS

Department of Mathematics, University of Athens, Panepistemiopolis 15784, Greece

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O. TALELLI

Department of Mathematics, University of Athens, Panepistemiopolis 15784, Greece

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, and

D. VARSOS

Department of Mathematics, University of Athens, Panepistemiopolis 15784, Greece

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https://doi.org/10.1142/S0218196704001797Cited by:1 (Source: Crossref)

Abstract

Here we characterize the residually finite groups G which are the fundamental groups of a finite graph of finitely generated torsion-free nilpotent groups. Namely we show that G is residually finite if and only if for each edge group of the graph of groups the two edge monomorphisms differ essentially by an isomorphism of certain subgroups of the Mal'cev completion of the corresponding vertex groups.

The authors acknowledge financial support from E.L.K.E.

Keywords:

AMSC: 20E06, 20E26, 20E08, 20F28

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