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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 1, Pages 37–74 (Mi izv1381)  

This article is cited in 7 scientific papers (total in 7 papers)

Some questions in the theory of varieties of groups

Yu. G. Kleiman


Abstract: In this paper a new method of studying identity relations in groups is described. Among the results obtained by this method is an example of a group variety that does not have an independent basis of identities. A conjecture by P. Hall on marginal subgroups is refuted. The question of the relation between the representation of a group variety in the form of a union and the product of two proper subvarieties is considered. An example of a group variety having a set of continuum many different covering varieties is constructed and a number of results are obtained, as corollaries, on whether (solvable) group varieties can be generated by certain classes of groups.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 22:1, 33–65

Bibliographic databases:

UDC: 519.4
MSC: Primary 20E10; Secondary 20E05, 20E26, 20F16
Received: 12.02.1981

Citation: Yu. G. Kleiman, “Some questions in the theory of varieties of groups”, Izv. Akad. Nauk SSSR Ser. Mat., 47:1 (1983), 37–74; Math. USSR-Izv., 22:1 (1984), 33–65

Citation in format AMSBIB
\Bibitem{Kle83}
\by Yu.~G.~Kleiman
\paper Some questions in the theory of varieties of groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 1
\pages 37--74
\mathnet{http://mi.mathnet.ru/izv1381}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=688918}
\zmath{https://zbmath.org/?q=an:0528.20025|0516.20014}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 22
\issue 1
\pages 33--65
\crossref{https://doi.org/10.1070/IM1984v022n01ABEH001433}


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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. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. I. Anokhin, “A basis of identities of a variety generated by a finitely-based quasi-variety of groups”, Sb. Math., 189:8 (1998), 1115–1124  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. M. I. Anokhin, “Embedding lattices in lattices of varieties of groups”, Izv. Math., 63:4 (1999), 649–665  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. Yu. Popov, “A Ring Variety without an Independent Basis”, Math. Notes, 69:5 (2001), 657–673  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. V. Yu. Popov, “O nezavisimo baziruemykh mnogoobraziyakh monoidov”, Fundament. i prikl. matem., 8:3 (2002), 829–876  mathnet  mathscinet  zmath
    6. V. Yu. Popov, “On Independently Partitionable Sets of Semigroup Identities”, Siberian Adv. Math., 14:2 (2004), 27–78  mathnet  mathscinet  elib
    7. V. Yu. Popov, “The Property of Having Independent Basis in Semigroup Varieties”, Algebra and Logic, 44:1 (2005), 46–54  mathnet  crossref  mathscinet  zmath  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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