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On subdirect products of type FPn of limit groups over Droms RAAGs
Published online by Cambridge University Press: 11 October 2023
Abstract
We generalise some known results for limit groups over free groups and residually free groups to limit groups over Droms RAAGs and residually Droms RAAGs, respectively. We show that limit groups over Droms RAAGs are free-by-(torsion-free nilpotent). We prove that if S is a full subdirect product of type $FP_s(\mathbb{Q})$ of limit groups over Droms RAAGs with trivial center, then the projection of S to the direct product of any s of the limit groups over Droms RAAGs has finite index. Moreover, we compute the growth of homology groups and the volume gradients for limit groups over Droms RAAGs in any dimension and for finitely presented residually Droms RAAGs of type $FP_m$ in dimensions up to m. In particular, this gives the values of the analytic $L^2$-Betti numbers of these groups in the respective dimensions.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 2 , March 2024 , pp. 417 - 440
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society