Skip to main content
Log in

Finite biprimary groups with all 3-maximal subgroups \({\mathfrak{U}}\)-subnormal

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

A complete classification of finite biprimary groups in which every 3-maximal subgroup is \({\mathfrak{U}}\)-subnormal is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Huppert B.: Normalteiler und maximale Untergruppen endlicher Gruppen. Math. Z. 60, 409–434 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  2. Asaad M.: Finite groups some whose n-maximal subgroups are normal. Acta Math. Hungar. 54, 9–27 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. R. Schmidt, Endliche Gruppen mit vielen modularen Untergruppen, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 34 (1969), 115–125.

  4. W. Guo, Yu. V. Lutsenko and A. N. Skiba, On nonnilpotent groups with every two 3-maximal subgroups permutable, Siberian Math. J., 50 (2009), 988–997.

  5. Yu. V. Lutsenko and A. N. Skiba, Finite groups with subnormal second and third maximal subgroups, Math. Notes, 91 (2012), 680–688.

  6. V. N. Kniahina and V. S. Monakhov, On the permutability of n-maximal subgroups with Schmidt subgroups, Trudy Inst. Mat. i Mekh. UrO RAN, 18 (2012), 125–130.

  7. V. A. Kovaleva and A. N. Skiba, Finite soluble groups with all n-maximal subgroups \({\mathfrak{F}}\)-subnormal, J. Group Theory, 17 (2014), 273–290.

  8. V. A. Kovaleva and X. Yi, Finite groups with all 3-maximal subgroups K-\({\mathfrak{U}}\)-subnormal, arXiv:1406.3464v1 [math.GR].

  9. Doerk K.: Minimal nicht uberauflosbare, endliche Gruppen. Math. Z. 91, 198–205 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  10. K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter (Berlin–New York, 1992).

  11. A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer-Verlag (Dordrecht, 2006).

  12. B. Huppert, Endliche Gruppen I, Springer-Verlag (Berlin–Heidelberg–New York, 1967).

  13. M. Weinstein (ed.), etc, Between Nilpotent and Solvable, Polygonal Publishing House (Passaic N.J., 1982).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to X. Yi.

Additional information

Research of Xiaolan Yi is supported by a NNSF grant of China (Grant # 11101369) and the Science Foundation of Zhejiang Sci–Tech University under grant 1013843-Y.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kovaleva, V.A., Yi, X. Finite biprimary groups with all 3-maximal subgroups \({\mathfrak{U}}\)-subnormal. Acta Math. Hungar. 146, 47–55 (2015). https://doi.org/10.1007/s10474-015-0498-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-015-0498-5

Key words and phrases

Mathematics Subject Classification

Navigation