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On groups with a small number of classes of conjugate noncomplemented subgroups

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Ukrainian Mathematical Journal Aims and scope

We give a description of finite nonprimary groups that contain at most two classes of conjugate noncomplemented subgroups.

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References

  1. P. Hall, “Complemented groups,” J. London Math. Soc., 12, 201–204 (1937).

    Article  MATH  Google Scholar 

  2. N. V. Baeva, “Completely factorizable groups,” Dokl. Akad. Nauk SSSR, 92, No. 5, 877–880 (1953).

    MathSciNet  MATH  Google Scholar 

  3. N. V. Chernikova, “Groups with complemented subgroups,” Mat. Sb., 39, 273–292 (1956).

    MathSciNet  Google Scholar 

  4. N. V. Chernikova, “On the main theorem on completely factorizable groups,” in: Groups with Systems of Complemented Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1972), pp. 49–58.

    Google Scholar 

  5. Yu. M. Gorchakov, “Primitive factorizable groups,” Uch. Zap. Perm. Univ., 17, 15–31 (1960).

    Google Scholar 

  6. S. N. Chernikov, “Groups with systems of complemented subgroups,” Mat. Sb., 35, 93–128 (1954).

    MathSciNet  Google Scholar 

  7. S. N. Chernikov, “Investigation of groups with given properties of subgroups,” Ukr. Mat. Zh., 21, No. 2, 193–209 (1969).

    Article  Google Scholar 

  8. O. Yu. Shmidt, “Groups having only one class of noninvariant subgroups,” Mat. Sb., 33, 161–172 (1926).

    MATH  Google Scholar 

  9. O. Yu. Shmidt, “Groups with two classes of noninvariant subgroups,” in: Proceedings of the Seminar on Group Theory [in Russian], Moscow (1938), pp. 7–26.

  10. P. P. Baryshovets and N. N. Bilotskii, “On groups with small number of classes of conjugate noncomplemented subgroups,” in: Abstracts of Ukrainian Mathematical Congress–2009 [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2009).

    Google Scholar 

  11. D. I. Zaitsev and O. N. Zub, “Groups with complemented abelian subgroups of nonprime orders,” in: Groups with Given Properties of Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1973), pp. 105–126.

    Google Scholar 

  12. M. Hall, Jr., The Theory of Groups [Russian translation], Inostrannaya Literatura, Moscow (1962).

    Google Scholar 

  13. O. N. Zub, “Groups whose noncyclic subgroups are complemented,” in: Groups with Restrictions for Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1971), pp. 134–158.

    Google Scholar 

  14. Ya. G. Berkovich, “Structure of a group and structure of its subgroups,” Dokl. Akad. Nauk SSSR, 179, No. 1, 13–16 (1968).

    MathSciNet  Google Scholar 

  15. P. P. Baryshovets, “On finite nonabelian groups with complemented nonabelian subgroups,” Ukr. Mat. Zh., 29, No. 6, 733–737 (1977).

    MathSciNet  MATH  Google Scholar 

  16. B. Huppert, Endliche Gruppen, I, Springer, Berlin (1967).

    MATH  Google Scholar 

  17. P. P. Baryshovets, “Finite nonnilpotent groups all nonabelian subgroups of which are complemented,” Ukr. Mat. Zh., 33, No. 2, 147–153 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  18. P. P. Baryshovets, “On one class of finite groups with complemented nonabelian subgroups,” Ukr. Mat. Zh., 33, No. 3, 291–296 (1981).

    MathSciNet  MATH  Google Scholar 

  19. G. A. Malan’ina, V. I. Khlebutina, and G. S. Shevtsov, “Finite minimal incompletely factorizable groups,” Mat. Zametki, 12, No. 2, 157–162 (1972).

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. National Aviation University, Kiev, Ukraine

    P. P. Baryshovets

  2. National Pedagogic University, Kiev, Ukraine

    N. N. Bilotskii

Authors
  1. P. P. Baryshovets
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  2. N. N. Bilotskii
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Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 10, pp. 1420–1427, October, 2010.

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Baryshovets, P.P., Bilotskii, N.N. On groups with a small number of classes of conjugate noncomplemented subgroups. Ukr Math J 62, 1649–1656 (2011). https://doi.org/10.1007/s11253-011-0456-5

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  • DOI: https://doi.org/10.1007/s11253-011-0456-5

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