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Publication Date:
February 2008
ISSN:
1435-4446
DOI:
10.1515/jgth.5.2.219

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Journal of Group Theory

Editor-in-Chief: Wilson, John S.

Managing Editor: Howie, James / Kramer, Linus / Parker, Christopher W.

Editorial Board Member: Abért, Miklós / Borovik, Alexandre V. / Boston, Nigel / Bridson, Martin R. / Caprace, Pierre-Emmanuel / Giovanni, Francesco / Guralnick, Robert / Jaikin Zapirain, Andrei / Kessar, Radha / Khukhro, Evgenii I. / Kochloukova, Dessislava H. / Malle, Gunter / Olshanskii, Alexander / Remy, Bertrand / Robinson, Derek J.S. / Willis, George

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Subgroups of constructive nilpotent-by-abelian groups and a generalization of a result of Bieri, Neumann and Strebel

Dessislava H Kochloukova1

1

Citation Information: Journal of Group Theory. Volume 5, Issue 2, Pages 219–232, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/jgth.5.2.219, February 2008

Publication History:
Received:
2000-08-31
Revised:
2001-09-11
Published Online:
2008-02-22

Abstract

We prove a ∑-version of the result of Bieri, Neumann and Strebel [R. Bieri, W. D. Neumann and R. Strebel. A geometric invariant of discrete groups. Invent. Math. 90 (1987), 451–477] that for a finitely presented group G without free subgroups of rank 2 the set ∑1(G)c has no antipodal points. More precisely, we prove that for such a group G

We show that if G is a finitely generated nilpotent-by-abelian group then

The latter result is used in constructing a counter-example to a conjecture of Meinert [H. Meinert. Iterated HNN-decomposition of constructible nilpotent-by-abelian groups. Comm. Algebra 23 (1995), 3155–3164] concerning the homological properties of subgroups of constructible nilpotent-by-abelian groups.

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