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Forum Mathematicum

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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 28, Issue 2 (Mar 2016)


On transfinite nilpotence of the Vogel–Levine localization

Roman Mikhailov
  • Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178 Russia; and St. Petersburg Department of Steklov Mathematical Institute, Russia
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Published Online: 2015-01-10 | DOI: https://doi.org/10.1515/forum-2014-0108


We construct a finitely-presented group such that its Vogel–Levine localization is not transfinitely nilpotent. This answers a problem of J. P. Levine.

Keywords: Vogel–Levine localization; transfinite nilpotence; group homology

MSC: 55P60; 20J05

About the article

Received: 2014-06-14

Published Online: 2015-01-10

Published in Print: 2016-03-01

Funding Source: Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University

Award identifier / Grant number: 11.G34.31.0026

Funding Source: JSC “Gazprom Neft”

Funding Source: RF Presidential

Award identifier / Grant number: MD-381.2014.1

Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0108.

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