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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 483–491
DOI: https://doi.org/10.4213/mzm8971 (Mi mzm8971) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups

D. N. Azarov

Ivanovo State University
Full-text PDF (432 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm8971
Abstract: A necessary and sufficient condition for the residual finiteness of a (generalized) free product of two residually finite solvable-by-finite minimax groups with cyclic amalgamated subgroups is obtained. This generalizes the well-known Dyer theorem claiming that every free product of two polycyclic-by-finite groups with cyclic amalgamated subgroups is a residually finite group.
Keywords: residually finite group, (generalized) free product with amalgamated subgroups, polycyclic-by-finite group, minimax group, solvable group, subnormal series, Chernikov group, Fitting subgroup, FATR group.
Received: 17.01.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 503–509
DOI: https://doi.org/10.1134/S0001434613030188
Bibliographic databases:
Document Type: Article
UDC: 512.543
Language: Russian
Citation: D. N. Azarov, “On the Residual Finiteness of Free Products of Solvable Minimax Groups with Cyclic Amalgamated Subgroups”, Mat. Zametki, 93:4 (2013), 483–491; Math. Notes, 93:4 (2013), 503–509
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    1. E. V. Sokolov, “On the Separability of Abelian Subgroups of the Fundamental Groups of Graphs of Groups. II”, Sib Math J, 65:1 (2024), 174  crossref
    2. E. V. Sokolov, “Ob otdelimosti abelevykh podgrupp fundamentalnykh grupp grafov grupp. II”, Sib. matem. zhurn., 65:1 (2024), 207–228  mathnet  crossref
    3. Evgeny Victorovich Sokolov, “On the separability of subgroups of nilpotent groups by root classes of groups”, Journal of Group Theory, 2023  crossref
    4. D. N. Azarov, “On the weak π-potency of some groups and free products”, Siberian Math. J., 61:6 (2020), 953–962  mathnet  crossref  crossref  isi  elib
    5. D. N. Azarov, “O finitnoi approksimiruemosti obobschennykh svobodnykh proizvedenii grupp s tsiklicheskim ob'edineniem”, Chebyshevskii sb., 14:3 (2013), 9–19  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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