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Publicly Available Published by De Gruyter July 14, 2009

On subdirect products of type FPm of limit groups

  • Dessislava H. Kochloukova
From the journal Journal of Group Theory

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.

Received: 2008-12-01
Revised: 2009-02-19
Published Online: 2009-07-14
Published in Print: 2010-January

© de Gruyter 2010

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