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On discrete homology of a free pro-$p$-group

Part of: Homotopy theory Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  07 September 2018

Sergei O. Ivanov  and
Roman Mikhailov
Sergei O. Ivanov
Affiliation:
Laboratory of Modern Algebra and Applications, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178 Russia email [email protected]
Roman Mikhailov
Affiliation:
Laboratory of Modern Algebra and Applications, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178 Russia St. Petersburg Department of Steklov Mathematical Institute, Russia email [email protected]
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Abstract

For a prime $p$, let $\hat{F}_{p}$ be a finitely generated free pro-$p$-group of rank at least $2$. We show that the second discrete homology group $H_{2}(\hat{F}_{p},\mathbb{Z}/p)$ is an uncountable $\mathbb{Z}/p$-vector space. This answers a problem of A. K. Bousfield.

Keywords

completionprofinite groupgroup homology

MSC classification

Primary: 55P60: Localization and completion 20E18: Limits, profinite groups
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 10 , October 2018 , pp. 2195 - 2204
Copyright
© The Authors 2018 

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