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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)

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
Received: 05.02.1988

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
\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
\jour Math. USSR-Sb.
\yr 1990
\vol 66
\issue 2
\pages 541--553

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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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. L. S. Kazarin, L. A. Kurdachenko, “Finiteness conditions and factorizations in infinite groups”, Russian Math. Surveys, 47:3 (1992), 81–126  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Obraztsov V., “On Infinite Complete Groups”, Commun. Algebr., 22:14 (1994), 5875–5887  crossref  mathscinet  zmath  isi
    4. Ivanov S., “On Some Finiteness Conditions in Semigroup and Group-Theory”, Semigr. Forum, 48:1 (1994), 28–36  crossref  mathscinet  isi
    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  isi
    7. Stonehewer S., Zacher G., “Dualities of Groups.”, Ann. Mat. Pura Appl., 170 (1996), 23–55  crossref  mathscinet  zmath  isi
    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  isi
    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  isi
    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. V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24  mathnet  crossref  mathscinet  isi
    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  mathnet
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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