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Acta Mathematica Hungarica

, Volume 136, Issue 1–2, pp 76–89 | Cite as

Finite groups with sn-embedded or s-embedded subgroups

  • Izabela Agata MalinowskaEmail author
Article

Abstract

A number of authors have studied the structure of a finite group G under the assumption that some subgroups of G are well located in G. We will generalize the notion of s-permutable and s-permutably embedded subgroups and we will obtain new criterions of p-nilpotency and supersolvability of groups. We also generalize some known results.

Key words and phrases

finite group permutable group s-embedded subgroup sn-embedded subgroup supersoluble group p-nilpotent group 

2000 Mathematics Subject Classification

20D10 20D20 

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References

  1. [1]
    M. Asaad, On the solvability of finite groups, Arch. Math., 51 (1988), 289–293. MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    M. Asaad, A. Ballester-Bolinches and M. C. Pedraza-Aguilera, A note on minimal subgroups of finite groups, Comm. Algebra, 24 (1996), 2771–2776. MathSciNetzbMATHGoogle Scholar
  3. [3]
    A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter (Berlin/New York, 2010). zbMATHCrossRefGoogle Scholar
  4. [4]
    A. Ballester-Bolinches and M. C. Pedraza-Aguilera, On minimal subgroups of finite groups, Acta Math. Hungar., 73 (1996), 335–342. MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    A. Ballester-Bolinches and M. C. Pedraza-Aguilera, Sufficient conditions for supersolubility of finite groups, J. Pure Appl. Algebra, 127 (1998), 113–118. MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    A. Ballester-Bolinches and Y. Wang, Finite groups with some c-normal minimal subgroups, J. Pure Appl. Algebra, 153 (2000), 121–127. MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    W. Guo, On \(\mathcal{F}\)-supplemented subgroups of finite groups, Manuscripta Math., 127 (2008), 139–150. MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    W. Guo, Y. Lu and W. Niu, s-embedded subgroups of finite groups, Algebra and Logic, 49 (2010), 293–304. MathSciNetCrossRefGoogle Scholar
  9. [9]
    W. Guo, K. P. Shum and A. N. Skiba, On solubility and supersolubility of some classes of finite groups, Sci. China Ser. A, 52 (2009), 272–286. MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    W. Guo and A. N. Skiba, Finite groups with given s-embedded and n-embedded subgroups, J. Algebra, 321 (2009), 2843–2860. MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    X. Y. Guo and K. P. Shum, Cover-avoidance properties and the structure of finite groups, J. Pure Appl. Algebra, 181 (2003), 297–308. MathSciNetCrossRefGoogle Scholar
  12. [12]
    L. P. Hao, The influence of X-s-semipermutable subgroups on the structure of finite groups, Southeast Asian Bulletin of Mathematics, 33 (2009), 421–432. MathSciNetzbMATHGoogle Scholar
  13. [13]
    B. Huppert, Endliche Gruppen I, Springer-Verlag (Berlin–New York, 1967). zbMATHCrossRefGoogle Scholar
  14. [14]
    Y. Li and Y. Wang, On π-quasinormally embedded subgroups of finite groups, J. Algebra, 281 (2004), 109–123. MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Y. M. Li, Y. M. Wang and H. Q. Wei, On p-nilpotency of finite groups with some subgroups π-quasinormally embedded, Acta Math. Hungar., 108 (2005), 283–298. MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    L. Miao and W. Guo, New criteria for p-nilpotency of finite groups, Comm. Algebra, 35 (2007), 965–974. MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    R. Ramadan, M. Ezzat Mohamed and A. A. Heliel, On c-normality of certain subgroups of prime order of finite groups, Arch. Math., 85 (2005), 203–210. MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    D. J. S. Robinson, A Course in the Theory of Groups, Springer–Verlag (New York, 1996). CrossRefGoogle Scholar
  19. [19]
    A. Shaalan, The influence of π-quasinormality of some subgroups on the structure of a finite group, Acta Math. Hungar., 56 (1990), 287–293. MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    L. A. Shemetkov, Formations of Finite Groups, Nauka (Moscow, 1978) (in Russian). zbMATHGoogle Scholar
  21. [21]
    Y. Wang, c-normality of groups and its properties, J. Algebra, 180 (1996), 954–965. MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    Y. Wang, Finite groups with some subgroups of Sylow subgroups c-supplemented, J. Algebra, 224 (2000), 467–478. MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    Y. Wang and W. Guo, Nearly s-normality of groups and its properties, Comm. Algebra, 38 (2010), 3821–3836. MathSciNetzbMATHCrossRefGoogle Scholar
  24. [24]
    H. Wei and Y. Wang, c -supplemented subgroups and p-nilpotency of finite groups, Ukrain. Mat. Zh., 59 (2007), 1121–1129. MathSciNetCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of BiałystokBiałystokPoland

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