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Mathematical Notes

, Volume 105, Issue 1–2, pp 251–257 | Cite as

Groups with Formation Subnormal 2-Maximal Subgroups

  • V. S. MonakhovEmail author
Article
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Abstract

Groups with X-subnormal 2-maximal subgroups are investigated for an arbitrary hereditary formation X. In such a group, all proper subgroups have nilpotent X-residuals. The cases in which X = A1F for some hereditary formation F or X is a solvable saturated formation are studied in more detail.

Keywords

finite group formation residual subnormal subgroup 

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References

  1. 1.
    V. S. Monakhov, Introduction to the Theory of Finite Groups and Their Classes (Vysh. Shkola, Minsk, 2006) [in Russian].Google Scholar
  2. 2.
    K. Doerk and T. Hawkes, Finite Soluble Groups (Walter de Gruyter, Berlin, 1992).CrossRefzbMATHGoogle Scholar
  3. 3.
    V. S. Monakhov and V. N. Kniahina, “Finite groups with P–subnormal subgroups,” Ric. Mat. 62 (2), 307–322 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    L. A. Shemetkov, Formations of Finite Groups (Nauka, Moscow, 1978) [in Russian].zbMATHGoogle Scholar
  5. 5.
    V. A. Kovaleva and A. N. Skiba, “Finite soluble groups with all n–maximal subgroups F–subnormal,” J. Group Theory 17 (2), 273–290 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    A. Ballester–Bolinches and L. M. Ezquerro, Classes of Finite Groups (Springer–Verlag, Dordrecht, 2006).zbMATHGoogle Scholar
  7. 7.
    V. S. Monakhov, “Schmidt subgroups, their existence and some applications,” in Ukrainian Mathematics Congress–2001 (Natsional. Akad. Nauk Ukraini, Inst. Mat., Kiev, 2002), Sec. 1, pp. 81–90 [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Francisk Skorina Gomel State UniversityGomelBelarus

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