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Detecting ends of residually finite groups in profinite completions
residually finite groups profinite completions Group Theory
2012/5/24
Let $\C$ be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\hookrightarrow G$ is a map of finitely generated residually $\C$ groups such that the induced map $\hat...
The following result is proved. Let w be a multilinear commutator and n a positive integer. Suppose that G is a resid-ually finite group in which every product of at most 896 w-values
has order divid...
Approximating the first $L^2$-betti number of residually finite groups
residually finite groups math
2010/11/24
We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an app...