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This article is cited in 6 papers
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
\mathnet{http://mi.mathnet.ru/msb2990}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=997899}
\zmath{http://www.zentralblatt-math.org/zmath/search/?an=Zbl 0685.20030|Zbl 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}
Linking options:
http://mi.mathnet.ru/eng/msb2990 http://mi.mathnet.ru/eng/msb/v180/i4/p529
 Full text (in Russian):
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References (in Russian):
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English version:
Mathematics of the USSR-Sbornik, 1990, 66:2, 541–553
Review databases:
 
ISI Web of Knowledge:
A1990DY49300015
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  ; V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182 -
Л. С. Казарин, Л. А. Курдаченко, “Условия конечности и факторизации в бесконечных группах”, УМН, 47:3(285) (1992), 75–114 ; L. S. Kazarin, L. A. Kurdachenko, “Finiteness conditions and factorizations in infinite groups”, Russian Math. Surveys, 47:3 (1992), 81–126
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Viatcheslav N. Obraztsov, “A new embedding scheme for groups and some applications”, J Austral Math Soc, 61:2 (1996), 267
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Dmitriy Sonkin, “CEP-Subgroups of Free Burnside Groups of Large Odd Exponents”, Communications in Algebra, 31:10 (2003), 4687
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M. De Falco, F. de Giovanni, C. Musella, “Groups in Which Every Subgroup Is Permutable-by-Finite”, Communications in Algebra, 32:3 (2004), 1007
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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 ; V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24
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