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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


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Online
ISSN
1435-4446
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Volume 13, Issue 1

Issues

On subdirect products of type FPm of limit groups

Dessislava H. Kochloukova
  • Department of Mathematics, Cx. P. 6065, University of Campinas (UNICAMP), 13083-970 Campinas, SP, Brazil. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-07-14 | DOI: https://doi.org/10.1515/jgt.2009.028

Abstract

We show that limit groups are free-by-(torsion-free nilpotent) and have non-positive Euler characteristic. We prove that for any non-abelian limit group the Bieri–Neumann–Strebel–Renz Σ-invariants are the empty set.

Let s ⩾ 3 be a natural number and G be a subdirect product of non-abelian limit groups intersecting each factor non-trivially. We show that the homology groups of any subgroup of finite index in G, in dimension is and with coefficients in ℚ, are finite-dimensional if and only if the projection of G to the direct product of any s of the limit groups has finite index. The case s = 2 is a deep result of M. Bridson, J. Howie, C. F. Miller III and H. Short.

About the article

Received: 2008-12-01

Revised: 2009-02-19

Published Online: 2009-07-14

Published in Print: 2010-01-01


Citation Information: Journal of Group Theory, Volume 13, Issue 1, Pages 1–19, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2009.028.

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Citing Articles

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[2]
Dessislava H. Kochloukova
São Paulo Journal of Mathematical Sciences, 2019, Volume 13, Number 1, Page 96
[3]
Dessislava H Kochloukova and Francismar Ferreira Lima
The Quarterly Journal of Mathematics, 2018, Volume 69, Number 3, Page 835
[4]
D. H. KOCHLOUKOVA and C. MARTÍNEZ–PÉREZ
Mathematical Proceedings of the Cambridge Philosophical Society, 2017, Page 1
[5]
Martin R. Bridson and Dessislava H. Kochloukova
Mathematische Annalen, 2017, Volume 367, Number 3-4, Page 1007
[6]
DESSISLAVA H. KOCHLOUKOVA and PAVEL A. ZALESSKII
Mathematical Proceedings of the Cambridge Philosophical Society, 2015, Volume 158, Number 02, Page 289
[7]
Dessislava Kochloukova and Pavel Zalesskii
Mathematische Nachrichten, 2015, Volume 288, Number 5-6, Page 604
[8]
Conchita Martínez-Pérez
Journal of Pure and Applied Algebra, 2014, Volume 218, Number 8, Page 1373
[9]
Ilir Snopce and Pavel A. Zalesskii
Selecta Mathematica, 2014, Volume 20, Number 2, Page 465
[10]
Dessislava H. Kochloukova and Hamish Short
Journal of Algebra, 2011, Volume 343, Number 1, Page 160
[11]
Daciberg Gonçalves and Dessislava Kochloukova
Pacific Journal of Mathematics, 2010, Volume 247, Number 2, Page 335

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