Skip to main content
SpringerLink
Log in

On weakly s-normal subgroups of finite groups

  • Published:
Ukrainian Mathematical Journal Aims and scope

Assume that G is a finite group and H is a subgroup of G: We say that H is s-permutably imbedded in G if, for every prime number p that divides |H|; a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; a subgroup H is s-semipermutable in G if HG p  = G p H for any Sylow p-subgroup G p of G with (p, |H|) = 1; a subgroup H is weakly s-normal in G if there are a subnormal subgroup T of G and a subgroup H * of H such that G = HT and H∩T ≤ H *; where H * is a subgroup of H that is either s-permutably imbedded or s-semipermutable in G. We investigate the influence of weakly s-normal subgroups on the structure of finite groups. Some recent results are generalized and unified.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Book  MATH  Google Scholar 

  2. O. H. Kegel, “Sylow-Gruppen and Subnormalteiler endlicher Gruppen,” Math. Z., 78, 205–221 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Wang, “On c-normality of groups and its properties,” J. Algebra, 180, 954–965 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. N. Skiba, “On weakly s-permutable subgroups of finite groups,” J. Algebra, 315, 192–209 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Ballester-Bolinches and M. C. Pedraza-Aguilera, “Sufficient conditions for supersolvability of finite groups,” J. Pure Appl. Algebra, 127, 113–118 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. Li, S. Qiao, and Y. Wang, “On weakly s-permutably embedded subgroups of finite groups,” Commun. Algebra, 37, No. 3, 1086–1097 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. Z. M. Chen, “On a theorem of Srinivasan,” J. Southwest Normal Univ. Nat. Sci., 12, No. 1, 1–4 (1987).

    Google Scholar 

  8. M. Asaad, “On maximal subgroups of Sylow subgroups of finite group,” Commun. Algebra, 26, 3647–3652 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Asaad and P. Csörgő, “Influence of minimal subgroups on the structure of finite group,” Arch. Math. (Basel), 72, 401–404 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Asaad, M. Ramadan, and A. Shaalan, “Influence of π-quasinormality on maximal subgroups of Sylow subgroups of Fitting subgroup of a finite group,” Arch. Math. (Basel), 56, 521–527 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Ballester-Bolinches and M. C. Pedraza-Aguilera, “On minimal subgroups of a finite group,” Acta Math. Hung., 73, 335–342 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Li and Y. Wang, “The influence of minimal subgroups on the structure of a finite group,” Proc. Am. Math. Soc., 131, 337–341 (2003).

    Article  MATH  Google Scholar 

  13. Y. Li and Y.Wang, “The influence of π-quasinormality of some subgroups of a finite group,” Arch. Math. (Basel), 81, 245–252 (2003).

    Article  MathSciNet  MATH  Google Scholar 

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

  15. B. Huppert and N. Blackburn, Finite Groups III, Springer, Berlin–New York (1982).

  16. A. Shaalan, “The influence of π-quasinormality of some subgroups on the structure of a finite group,” Acta Math. Hung., 56, 287–293 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  17. L. Wang and Y. Wang, “On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups,” Commun. Algebra, 34, 143–149 (2006).

    Article  MATH  Google Scholar 

  18. H. Wei, Y. Wang, and Y. Li, “On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups,” Commun. Algebra, 31, 4807–4816 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  19. Q. Zhang and L. Wang, “The influence of s-semipermutable subgroups on the structure of a finite group,” Acta Math. Sinica (Chin. Ser.), 48, 81–88 (2005)

    Google Scholar 

  20. Y. Li and Y. Wang, “On π-quasinormally embedded subgroups of finite groups,” J. Algebra, 281, 109–123 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  21. Y. Li, Y. Wang, and H. Wei, “On p-nilpotency of finite groups with some subgroups π-quasinormally embedded,” Acta Math. Hung., 108, No. 4, 283–298 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  22. Y. Li, X. He, and Y. Wang, “On s-semipermutable subgroups of finite groups,” Acta Math. Sinica, Eng. Ser., 26, No. 11, 2215–2222 (2010).

  23. Y. Li, “On s-semipermutable and c-normal subgroups of finite groups,” Arab. J. Sci. Eng. Sect. A Sci., 34, No. 2, 1–9 (2009).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Guangdong University of Education, Guangzhou, China

    Y. Li

  2. Yunnan University, Kunming, China

    S. Qiao

Authors
  1. Y. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 11, pp. 1555–1564, November, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y., Qiao, S. On weakly s-normal subgroups of finite groups. Ukr Math J 63, 1770–1780 (2012). https://doi.org/10.1007/s11253-012-0612-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-012-0612-6

Keywords

Search

Navigation