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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 28, Issue 2


A one-relator group with long lower central series

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-2014-0107


A one-relator group with lower central series of length ω2 is constructed. This answers a problem of G. Baumslag.

Keywords: One-relator group; transfinite nilpotence; lower central series

MSC: 20B07

About the article

Received: 2014-06-14

Revised: 2014-09-18

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, Volume 28, Issue 2, Pages 327–331, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0107.

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