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Sibirsk. Mat. Zh., 2017, Volume 58, Number 3, Pages 700–709 (Mi smj2890)  

This article is cited in 4 scientific papers (total in 4 papers)

The root class residuality of Baumslag–Solitar groups

E. A. Tumanova

Ivanovo State University, Ivanovo, Russia

Abstract: Given a homomorphically closed root class $\mathscr K$ of groups, we find a criterion for a Baumslag–Solitar group to be a residually $\mathscr K$-group. In particular, we establish that all Baumslag–Solitar groups are residually soluble and a Baumslag–Solitar group is residually finite soluble if and only if it is residually finite.

Keywords: root class residuality, residual solubility, residual $\pi$-finiteness, Baumslag–Solitar groups, HNN-extension.

Funding Agency Grant Number
Ivanovo State University
The author was supported by Ivanovo State University.


DOI: https://doi.org/10.17377/smzh.2017.58.317

Full text: PDF file (297 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:3, 546–552

Bibliographic databases:

UDC: 512.543
MSC: 20E26, 20E06, 20F22
Received: 22.06.2016

Citation: E. A. Tumanova, “The root class residuality of Baumslag–Solitar groups”, Sibirsk. Mat. Zh., 58:3 (2017), 700–709; Siberian Math. J., 58:3 (2017), 546–552

Citation in format AMSBIB
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\paper The root class residuality of Baumslag--Solitar groups
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Sokolov, E. A. Tumanova, “Root Class Residuality of HNN-Extensions with Central Cyclic Associated Subgroups”, Math. Notes, 102:4 (2017), 556–568  mathnet  crossref  crossref  mathscinet  isi  elib
    2. E. A. Tumanova, “The root class residuality of the tree product of groups with amalgamated retracts”, Siberian Math. J., 60:4 (2019), 699–708  mathnet  crossref  crossref  isi  elib
    3. E. V. Sokolov, E. A. Tumanova, “Obobschennye pryamye proizvedeniya grupp i ikh primenenie k izucheniyu approksimiruemosti svobodnykh konstruktsii grupp”, Algebra i logika, 58:6 (2019), 720–740  mathnet  crossref
    4. E. V. Sokolov, E. A. Tumanova, “Ob approksimiruemosti kornevymi klassami nekotorykh svobodnykh proizvedenii grupp s normalnymi ob'edinennymi podgruppami”, Izv. vuzov. Matem., 2020, no. 3, 48–63  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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