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

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.

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

Bibliographic databases:

UDC: 512.543
MSC: Primary 20E32; Secondary 20E06

Citation: V. N. Obraztsov, “An imbedding theorem for groups and its corollaries”, Mat. Sb., 180:4 (1989), 529–541; Math. USSR-Sb., 66:2 (1990), 541–553

Citation in format AMSBIB
\Bibitem{Obr89}
\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{https://zbmath.org/?q=an:0685.20030|0698.20021}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 66
\issue 2
\pages 541--553
\crossref{https://doi.org/10.1070/SM1990v066n02ABEH001184}


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Citing articles on Google Scholar: Russian citations, English citations
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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
2. L. S. Kazarin, L. A. Kurdachenko, “Finiteness conditions and factorizations in infinite groups”, Russian Math. Surveys, 47:3 (1992), 81–126
3. Obraztsov V., “On Infinite Complete Groups”, Commun. Algebr., 22:14 (1994), 5875–5887
4. Ivanov S., “On Some Finiteness Conditions in Semigroup and Group-Theory”, Semigr. Forum, 48:1 (1994), 28–36
5. Viatcheslav N. Obraztsov, “A new embedding scheme for groups and some applications”, J Austral Math Soc, 61:2 (1996), 267
6. Obraztsov V., “Embedding Into Groups with Well-Described Lattices of Subgroups”, Bull. Aust. Math. Soc., 54:2 (1996), 221–240
7. Stonehewer S., Zacher G., “Dualities of Groups.”, Ann. Mat. Pura Appl., 170 (1996), 23–55
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
9. Herzog M., Longobardi P., Maj M., Mann A., “On Generalized Dedekind Groups and Tarski Super Monsters”, J. Algebra, 226:2 (2000), 690–713
10. Dmitriy Sonkin, “CEP-Subgroups of Free Burnside Groups of Large Odd Exponents”, Communications in Algebra, 31:10 (2003), 4687
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
12. V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24
13. L. A. Kurdachenko, I. Ya. Subbotin, N. A. Turbay, “On influence of formation theory concepts and ideology on infinite group theory”, Tr. In-ta matem., 21:1 (2013), 69–77
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