Abstract
A group Γ has type F Pn if a trivial ℤΓ-module ℤ has a projective resolution P:…Pn → … → P1 → P0 → ℤ in which ℤΓ-module Pn,…P1, P0 are finitely generated. Let the finitely generated group Γ be a split extension of the Abelian group M by an Abelian group Q, suppose M is torsion free, and assume Γ∈F Pm, m≥2. Then the invariant ∑ Mc is m-tame.
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Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 194–218, March–April, 1997.
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Noskov, G.A. The bieri-strebel invariant and homological finiteness conditions for metabelian groups. Algebr Logic 36, 117–132 (1997). https://doi.org/10.1007/BF02672479
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DOI: https://doi.org/10.1007/BF02672479