The virtual first Betti number of soluble groups
نویسندگان
چکیده
منابع مشابه
Betti Number Estimates for Nilpotent Groups
We prove an extension of the following result of Lubotzky and Madid on the rational cohomology of a nilpotent group G: If b1 < ∞ and G⊗Q = 0,Q,Q then b2 > b1/4. Here the bi are the rational Betti numbers of G and G ⊗ Q denotes the Malcev-completion of G. In the extension, the bound is improved when the relations of G are known to all have at least a certain commutator length. As an application ...
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Let G be a finitely generated group and G = G0 ⊇ G1 ⊇ G2 ⊇ · · · a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b1(Gi;K) [G:Gi] of normalized first Betti numbers of Gi with coefficients in K, which we call a K-approximation for b (2) 1 (G), the first L2-Betti number of G. In this paper we address the questions of when Qapproximation and Fp-ap...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2015
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2015.274.497