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Mat. Sb., 1989, Volume 180, Number 4, Pages 529–541 (Mi msb2990)  

This article is cited in 13 scientific papers (total in 13 papers)


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An imbedding theorem for groups and its corollaries

V. N. Obraztsov


Abstract: An “economical” imbedding theorem is proved for at most a denumerable set of groups of finite or denumerable cardinality without involution in a group with “few” subgroups. This result is used to solve a series of problems about groups satisfying the descending chain condition for subgroups; in particular, a nondenumerable group with this condition is constructed.
Bibliography: 20 titles.

UDC: 512.543

MSC: Primary 20E32; Secondary 20E06

Received: 05.02.1988

Citation: V. N. Obraztsov, “An imbedding theorem for groups and its corollaries”, Mat. Sb., 180:4 (1989), 529–541

Citation in format AMSBIB
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\by V.~N.~Obraztsov
\paper An imbedding theorem for groups and its corollaries
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 4
\pages 529--541
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=997899}
\zmath{http://zbmath.org/?q=an:0685.20030|0698.20021}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 66
\issue 2
\pages 541--553
\crossref{http://dx.doi.org/10.1070/SM1990v066n02ABEH001184}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990DY49300015}


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  • http://mi.mathnet.ru/eng/msb2990
  • http://mi.mathnet.ru/eng/msb/v180/i4/p529

    Full text (in Russian): PDF file (1683 kB)
    References (in Russian): PDF file   HTML файл

    English version:
    Mathematics of the USSR-Sbornik, 1990, 66:2, 541–553

    Review databases:
    ISI Web of Knowledge: A1990DY49300015

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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. В. Д. Мазуров, “Решенные задачи “Коуровской тетради””, УМН, 46:5(281) (1991), 121–156  mathnet  mathscinet  zmath  adsnasa; V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  crossref
    2. Л. С. Казарин, Л. А. Курдаченко, “Условия конечности и факторизации в бесконечных группах”, УМН, 47:3(285) (1992), 75–114  mathnet  mathscinet  zmath  adsnasa; L. S. Kazarin, L. A. Kurdachenko, “Finiteness conditions and factorizations in infinite groups”, Russian Math. Surveys, 47:3 (1992), 81–126  crossref
    3. Obraztsov V., “On Infinite Complete Groups”, Commun. Algebr., 22:14 (1994), 5875–5887  crossref  mathscinet  zmath
    4. Ivanov S., “On Some Finiteness Conditions in Semigroup and Group-Theory”, Semigr. Forum, 48:1 (1994), 28–36  crossref  mathscinet
    5. Viatcheslav N. Obraztsov, “A new embedding scheme for groups and some applications”, J Austral Math Soc, 61:2 (1996), 267  crossref
    6. Obraztsov V., “Embedding Into Groups with Well-Described Lattices of Subgroups”, Bull. Aust. Math. Soc., 54:2 (1996), 221–240  crossref  mathscinet  zmath
    7. Stonehewer S., Zacher G., “Dualities of Groups.”, Ann. Mat. Pura Appl., 170 (1996), 23–55  crossref  mathscinet  zmath
    8. Obraztsov V., “Simple Torsion-Free Groups in Which the Intersection of Any Two Non-Trivial Subgroups Is Non-Trivial”, J. Algebra, 199:1 (1998), 337–343  crossref  mathscinet  zmath
    9. Herzog M., Longobardi P., Maj M., Mann A., “On Generalized Dedekind Groups and Tarski Super Monsters”, J. Algebra, 226:2 (2000), 690–713  crossref  mathscinet  zmath
    10. Dmitriy Sonkin, “CEP-Subgroups of Free Burnside Groups of Large Odd Exponents”, Communications in Algebra, 31:10 (2003), 4687  crossref
    11. M. De Falco, F. de Giovanni, C. Musella, “Groups in Which Every Subgroup Is Permutable-by-Finite”, Communications in Algebra, 32:3 (2004), 1007  crossref
    12. В. С. Атабекян, “О нормальных подгруппах в периодических произведениях С. И. Адяна”, Алгоритмические вопросы алгебры и логики, Сборник статей. К 80-летию со дня рождения академика Сергея Ивановича Адяна, Тр. МИАН, 274, МАИК, М., 2011, 15–31  mathnet  mathscinet; V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24  crossref
    13. L. A. Kurdachenko, I. Ya. Subbotin, N. A. Turbay, “On influence of formation theory concepts and ideology on infinite group theory”, Тр. Ин-та матем., 21:1 (2013), 69–77  mathnet
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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