The first -Betti number and approximation in arbitrary characteristic
Mikhail Ershov
Wolfgang Lück
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Abstract
Let be a finitely generated group and a descending chain of finite index normal subgroups of . Given a field , we consider the sequence of normalized first Betti numbers of with coefficients in , which we call a -approximation for , the first -Betti number of . In this paper we address the questions of when -approximation and -approximation have a limit, when these limits coincide, when they are independent of the sequence and how they are related to . In particular, we prove the inequality under the assumptions that and each is a finite -group.
Cite this article
Mikhail Ershov, Wolfgang Lück, The first -Betti number and approximation in arbitrary characteristic. Doc. Math. 19 (2014), pp. 313–331
DOI 10.4171/DM/448