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Algebra Logika, 2020, Volume 59, Number 4, Pages 413–431 (Mi al2624)  

Lower central series of Baumslag–Solitar groups

V. G. Bardakovabcd, M. V. Neshchadimbdc

a Novosibirsk State Agrarian University
b Tomsk State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d Novosibirsk State University

Abstract: We look at Baumslag–Solitar groups. Lower central series are given for residually nilpotent Baumslag–Solitar groups. For some Baumslag–Solitar groups that are not residually nilpotent, we find the intersection of all terms of the lower central series. Also we point out non-Abelian Baumslag–Solitar groups having lower central series of length 2. For some Baumslag–Solitar groups, a relationship is established between an intersection of subgroups of finite index and an intersection of terms of the lower central series.

Keywords: Baumslag–Solitar groups, residual nilpotency, lower central series.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00569
18-01-00057_а
M. V. Neshchadim is Supported by RFBR, project No. 19-01-00569. V. G. Bardakov is Supported by RFBR, project No. 18-01-00057.


DOI: https://doi.org/10.33048/alglog.2020.59.401

Full text: PDF file (249 kB)
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English version:
Algebra and Logic, 2020, 59:4, 281–294

Bibliographic databases:

UDC: 512.7
Received: 19.09.2019
Revised: 24.11.2020

Citation: V. G. Bardakov, M. V. Neshchadim, “Lower central series of Baumslag–Solitar groups”, Algebra Logika, 59:4 (2020), 413–431; Algebra and Logic, 59:4 (2020), 281–294

Citation in format AMSBIB
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\paper Lower central series of Baumslag--Solitar groups
\jour Algebra Logika
\yr 2020
\vol 59
\issue 4
\pages 413--431
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\crossref{https://doi.org/10.33048/alglog.2020.59.401}
\transl
\jour Algebra and Logic
\yr 2020
\vol 59
\issue 4
\pages 281--294
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