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Algebra Logika, 2017, Volume 56, Number 2, Pages 164–175 (Mi al786)  

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

The criterion of Shmel'kin and varieties generated by wreath products of finite groups

V. H. Mikaelianab

a Yerevan State University, ul. Alex Manoogian 1, Yerevan, 0025 Armenia
b American University of Armenia, pr. Marshala Bagramyana 40, Yerevan, 0019 Armenia

Abstract: We present a general criterion under which the equality $\operatorname{var}(A\operatorname{wr}B)=\operatorname{var}(A)\operatorname{var}(B)$ holds for finite groups $A$ and $B$. This generalizes some known results in this direction and continues our previous research [J. Algebra, 313, No. 2 (2007), 455–458] on varieties generated by wreath products of Abelian groups. The classification is based on the techniques developed by A. L. Shmel'kin, R. Burns, etc., who used critical groups, verbal wreath products, and Cross properties for studying critical groups in nilpotent-by-Abelian varieties.

Keywords: wreath products, varieties of groups, finite groups, products of varieties of groups, Abelian groups, nilpotent groups, critical groups, Cross varieties.

Funding Agency Grant Number
Russian Foundation for Basic Research 15RF-054
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 15T-1A258
Supported by RFBR and SCS MES RA (joint project 15RF-054) and by SCS MES RA (grant 15T-1A258).


DOI: https://doi.org/10.17377/alglog.2017.56.203

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English version:
Algebra and Logic, 2017, 56:2, 108–115

Bibliographic databases:

UDC: 512.543.27+512.543.56
Received: 04.10.2015

Citation: V. H. Mikaelian, “The criterion of Shmel'kin and varieties generated by wreath products of finite groups”, Algebra Logika, 56:2 (2017), 164–175; Algebra and Logic, 56:2 (2017), 108–115

Citation in format AMSBIB
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\by V.~H.~Mikaelian
\paper The criterion of Shmel'kin and varieties generated by wreath products of finite groups
\jour Algebra Logika
\yr 2017
\vol 56
\issue 2
\pages 164--175
\mathnet{http://mi.mathnet.ru/al786}
\crossref{https://doi.org/10.17377/alglog.2017.56.203}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3744779}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 2
\pages 108--115
\crossref{https://doi.org/10.1007/s10469-017-9433-x}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85022211408}


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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. V. H. Mikaelian, “On the classification of varieties generated by wreath products of groups”, Izv. Math., 82:5 (2018), 1006–1018  mathnet  crossref  crossref  adsnasa  isi  elib
    2. V. H. Mikaelian, “$K_p$-series and varieties generated by wreath products of $p$-groups”, Int. J. Algebr. Comput., 28:8, SI (2018), 1693–1703  crossref  mathscinet  zmath  isi  scopus
    3. V. H. Mikaelian, “Subvariety structures in certain product varieties of groups”, J. Group Theory, 21:5 (2018), 865–884  crossref  mathscinet  zmath  isi
    4. V S. Ludkowski, “Smashed and twisted wreath products of metagroups”, Axioms, 8:4 (2019), 127  crossref  isi  scopus
  • Алгебра и логика Algebra and Logic
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