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On complemented subgroups of finite groups

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Abstract

A subgroup H of a group G is said to be complemented in G if there exists a subgroup K of G such that G = HK and H ⋂ K = 1. In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about p-nilpotent groups.

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References

  1. Z. Arad, M. B. Ward: New criteria for the solvability of finite groups. J. Algebra 77 (1982), 234–246.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Ballester-Bolinches, X. Guo: On complemented subgroups of finite groups. Arch. Math. 72 (1999), 161–166.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Gross: Conjugacy of odd order Hall subgroup. Bull. London Math. Soc. 19 (1987), 311–319.

    MATH  MathSciNet  Google Scholar 

  4. W. Guo: The Theory of Classes of Groups. Kluwer Academic Publishers, Beijing-New York-Dordrecht-Boston-London, 2000.

    MATH  Google Scholar 

  5. W. Guo: The influence of minimal subgroups on the structure of finite groups. Southeast Asian Bulletin of Mathematics 22 (1998), 287–290.

    MATH  MathSciNet  Google Scholar 

  6. P. Hall: A characteristic property of soluble groups. J. London Math. Soc. 12 (1937), 188–200.

    Google Scholar 

  7. B. Huppert: Endliche Gruppen I. Springer-Verlag, Berlin-Heidelberg-New York, 1967.

    MATH  Google Scholar 

  8. O. H. Kegel: On Huppert’s characterization of finite supersoluble groups. In: Proc. Internat. Conf. Theory Groups, Canberra, 1965. New York, 1967, pp. 209–215.

  9. O. H. Kegel: Produkte nilpotenter gruppen. Arch. Math. 12 (1961), 90–93.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. J. Robinson: A Course in the Theory of Groups. Springer-Verlag, Berlin-New York, 1993.

    MATH  Google Scholar 

  11. Y. Wang: Finite groups with some subgroups of Sylow subgroups c-supplemented. J. Algebra 224 (2000), 467–478.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. Xu: An Introduction to Finite Groups. Science Press, Beijing, 1999. (In Chinese.)

    Google Scholar 

  13. Y. Zhang: The Structure of Finite Groups. Science Press, Beijing, 1982. (In Chinese.)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Yangzhou University, Yangzhou, 225002, P.R. China

    Long Miao

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  1. Long Miao
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Miao, L. On complemented subgroups of finite groups. Czech Math J 56, 1019–1028 (2006). https://doi.org/10.1007/s10587-006-0077-6

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  • DOI: https://doi.org/10.1007/s10587-006-0077-6

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