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Algebra Logika, 2019, Volume 58, Number 6, Pages 720–740 (Mi al926)  

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

Generalized direct products of groups and their application to the study of residuality of free constructions of groups

E. V. Sokolov, E. A. Tumanova

Ivanovo State University

Abstract: We introduce the construction of a generalized direct product associated with a graph of groups and prove two sufficient conditions for its existence. These results are applied to obtain some sufficient conditions for an $\mathrm{HNN}$-extension with central associated subgroups to be residually a $\mathcal{C}$-group where $\mathcal{C}$ is a root class of groups. In particular, it is proved that an $\mathrm{HNN}$-extension of a solvable group with central associated subgroups is residually solvable.

Keywords: generalized direct product, generalized free product, $\mathrm{HNN}$-extension, residual finiteness, residual $p$-finiteness, residual solvability, root-class residuality.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00187
Supported by RFBR, project No. 18-31-00187.


DOI: https://doi.org/10.33048/alglog.2019.58.604

Full text: PDF file (265 kB)
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English version:
Algebra and Logic, 2020, 58:6, 480–493

Bibliographic databases:

UDC: 512.543
Received: 12.02.2019
Revised: 12.02.2020

Citation: E. V. Sokolov, E. A. Tumanova, “Generalized direct products of groups and their application to the study of residuality of free constructions of groups”, Algebra Logika, 58:6 (2019), 720–740; Algebra and Logic, 58:6 (2020), 480–493

Citation in format AMSBIB
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\by E.~V.~Sokolov, E.~A.~Tumanova
\paper Generalized direct products of groups and their application to the study of residuality of free constructions of groups
\jour Algebra Logika
\yr 2019
\vol 58
\issue 6
\pages 720--740
\mathnet{http://mi.mathnet.ru/al926}
\crossref{https://doi.org/10.33048/alglog.2019.58.604}
\transl
\jour Algebra and Logic
\yr 2020
\vol 58
\issue 6
\pages 480--493
\crossref{https://doi.org/10.1007/s10469-020-09568-x}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85081548374}


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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, “Ob approksimiruemosti kornevymi klassami drevesnykh proizvedenii s tsentralnymi ob'edinennymi podgruppami”, Sib. matem. zhurn., 61:3 (2020), 692–702  mathnet  crossref
    2. E. A. Tumanova, “On the root-class residuality of certain HNN-extensions of groups”, Russian Math. (Iz. VUZ), 64:12 (2020), 38–45  mathnet  crossref  crossref  isi
    3. E. A. Tumanova, “On the residual properties of generalized direct products of groups”, Lobachevskii J. Math., 41:9, SI (2020), 1704–1711  crossref  mathscinet  zmath  isi  scopus
    4. E. V. Sokolov, “Ob approksimiruemosti kornevymi klassami fundamentalnykh grupp grafov grupp”, Sib. matem. zhurn., 62:4 (2021), 878–893  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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