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Ukrainian Mathematical Journal

, Volume 65, Issue 11, pp 1599–1611 | Cite as

On Infinite Groups with Complemented Non-Abelian Subgroups

  • P. P. Baryshovets
Article
  • 47 Downloads

We present the description of locally finite groups containing at least one non-Abelian Sylow subgroup in which all non-Abelian subgroups are complemented.

Keywords

Abelian Group Finite Group Sylow Subgroup Quotient Group Abelian Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Hall, “Complemented groups,” J. London Math. Soc., 12, 201–204 (1937).CrossRefGoogle Scholar
  2. 2.
    N. V. Baeva, “Completely factorizable groups,” Dokl. Akad. Nauk SSSR, 92, No. 5, 877–880 (1953).zbMATHMathSciNetGoogle Scholar
  3. 3.
    N. V. Chernikova, “Groups with complemented subgroups,” Mat. Sb., 39, 273–292 (1956).MathSciNetGoogle Scholar
  4. 4.
    N. V. Chernikova, “On the main theorem on completely factorizable groups,” in: Groups with Systems of Complemented Subgroups [in Russian], Institute of Mathematics, Academy of Sciences of Ukr. SSR, Kiev (1972), pp. 49–58.Google Scholar
  5. 5.
    S. N. Chernikov, “Groups with systems of complemented subgroups,” Mat. Sb., 35, 93–128 (1954).MathSciNetGoogle Scholar
  6. 6.
    Yu. M. Gorchakov, “Primitive-factorizable groups,” Uchen. Zap. Perm. Univ., 17, Issue 2, 15–31 (1960).Google Scholar
  7. 7.
    S. N. Chernikov, “Investigation of groups with given properties of the subgroups,” Ukr. Mat. Zh., 21, No. 2, 193–209 (1969); English translation: Ukr. Math. J., 21, No. 2, 160–172 (1969).CrossRefGoogle Scholar
  8. 8.
    P. Hall, “A characteristic property of soluble groups,” J. London Math. Soc., 12, 198–200 (1937).CrossRefGoogle Scholar
  9. 9.
    S. N. Chernikov, Groups with Given Properties of a System of Subgroups [in Russian], Nauka, Moscow (1980).Google Scholar
  10. 10.
    D. I. Zaitsev, “Direct sums of infinite Abelian groups with operators,” Ukr. Mat. Zh., 40, No. 3, 303–309 (1988); English translation: Ukr. Math. J., 40, No. 3, 257–263 (1988).Google Scholar
  11. 11.
    Ya. P. Sysak, Products of Infinite Groups [in Russian], Preprint No. 82.53, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1982).Google Scholar
  12. 12.
    N. S. Chernikov, Groups Decomposable in the Products of Permutable Subgroups [in Russian], Naukova Dumka, Kiev (1987).Google Scholar
  13. 13.
    O. N. Zub, “Groups whose noncyclic subgroups are complemented,” in: Groups with Restrictions for Subgroups [in Russian], Naukova Dumka, Kiev (1971), pp. 134–159.Google Scholar
  14. 14.
    É. S. Alekseeva, “Infinite nonprimary factorizable groups,” in: Some Problems of the Theory of Groups [in Russian], Institute of Mathematics, Academy of Sciences of Ukr. SSR, Kiev (1975), pp. 123–140.Google Scholar
  15. 15.
    N. M. Suchkov, “On some linear groups with complemented subgroups,” Algebra Logika, 16, No. 5, 603–620 (1977).CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    P. P. Baryshovets, “Finite non-Abelian 2-groups with complemented non-Abelian subgroups,” in: Group-Theoretic Investigations [in Russian], Naukova Dumka, Kiev (1978), pp. 34–50.Google Scholar
  17. 17.
    P. P. Baryshovets, “On finite non-Abelian p-groups with complemented non-Abelian subgroups,” in: Structure of the Groups and the Properties of Their Subgroups [in Russian], Institute of Mathematics, Academy of Sciences of Ukr. SSR, Kiev (1978), pp. 39– 62.Google Scholar
  18. 18.
    P. P. Baryshovets, “Finite non-Abelian groups with complemented non-Abelian subgroups,” Ukr. Mat. Zh., 29, No. 6, 733–737 (1977); English translation: Ukr. Math. J., 29, No. 6, 541–544 (1977).zbMATHMathSciNetGoogle Scholar
  19. 19.
    P. P. Baryshovets, “Finite nonnilpotent groups all non-Abelian subgroups of which can be complemented,” Ukr. Mat. Zh., 33, No. 2, 147–153 (1981); English translation: Ukr. Math. J., 33, No. 2, 117–122 (1981).CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    D. Taunt, “On A-groups,” Proc. Cambridge Phil. Soc., 45, No. 1, 24–42 (1949).CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    S. N. Chernikov, “Infinite locally soluble groups,” Mat. Sb., 49, No. 7, 35–64 (1940).Google Scholar
  22. 22.
    A. G. Kurosh, The Theory of Groups [in Russian], Nauka, Moscow (1967).Google Scholar
  23. 23.
    B. I. Mishchenko, “Locally graded groups with complemented infinite non-Abelian subgroups,” Ukr. Mat. Zh., 43, No. 7-8, 1098– 1100 (1991); English translation: Ukr. Math. J., 43, No. 7-8, 1031–1033 (1991).MathSciNetGoogle Scholar
  24. 24.
    J. Dixon, “Complements of normal subgroups in infinite groups,” Proc. London Math. Soc., 17, 431–446 (1967).CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    J. Dixon, “Corrigenda. Complements of normal subgroups in infinite groups,” Proc. London Math. Soc., 18, 768 (1968).CrossRefMathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • P. P. Baryshovets
    • 1
  1. 1.National Aviation UniversityKievUkraine

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