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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...
Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions
Ascending HNN extensions of polycyclic groups profinite completions
2010/12/6
Assume G is a polycyclic group and : G → G an endomorphism. Let G∗ be the ascending HNN extension of G with respect to ; that is, G∗ is given by the presentation G∗ = hG, | t...