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Complemented Sylow subgroups of finite groups

Funds:  Supported by the NSFC (11871062, 11501235), the Natural Science Foundation of Jiangsu Province (BK20181451), the Key Natural Science Foundation of Anhui Education Commission (KJ2017A569), the Fundamental Research Funds of China West Normal University (17E091).
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https://doi.org/10.3969/j.issn.0253-2778.2018.11.005
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  • Author Bio:

    BAO Hongwei, male, born in 1970, master/associate Prof. Research field:Finite group theory. E-mail: big_bao2003@163.com

  • Corresponding author: ZHANG Jia
  • Received Date: 08 July 2017
  • Accepted Date: 05 January 2018
  • Rev Recd Date: 05 January 2018
  • Publish Date: 30 November 2018
    Abstract

  • Abstract

    The relationship between the complementability of Sylow subgroups and the structure of a group was considered, and some results about the construction of composition factors were obtained. Further, one of Heliel’s results is the corollary of our results.

    Abstract

    The relationship between the complementability of Sylow subgroups and the structure of a group was considered, and some results about the construction of composition factors were obtained. Further, one of Heliel’s results is the corollary of our results.
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    • References(13)
  • [1]
    DOERK K, HAWKES T. Finite Soluble Groups[M]. Berlin/ New York: Walter de Gruyter, 1992.
    [2]
    HUPPERT B, BLACKBURN N. Finite Groups Ⅲ[M]. Berlin/ New York: Springer-Verlag, 1982.
    [3]
    HALL P. A characteristic property of solvable groups[J]. J London Math Soc,1937,12: 188-200.
    [4]
    ARAD Z, WARD M B. New criteria for the solvability of finite groups[J]. J Algebra, 1982, 77: 234-246.
    [5]
    BALLESTER-BOLINCHES A, GUO X. On complemented subgroups of finite groups[J]. Arch Math, 1999, 72: 161-166.
    [6]
    QIAN G, TANG F. Finite groups with certain subgroups of prime power order complemented[J]. J Algebra, 2015, 423: 950-962.
    [7]
    MONAKHOV V S, KNIAHINA V N. Finite groups with complemented subgroups of prime orders[J]. J Group Theory, 2015, 18: 905-912.
    [8]
    ASAAD M. Finite groups with certain subgroups of Sylow subgroups complemented[J]. J Algebra, 2010, 323: 1958-1965.
    [9]
    GURALNICK R. Subgroups of prime power index in a simple group[J]. J Algebra, 1983, 811: 304-311.
    [10]
    GUO W. The Theory of Classes of Groups[M]. Beijing/ New York/ Dordrecht/ Boston/ London: Science Press/ Kluwer Academic Publishers, 2000.
    [11]
    BUGEAUD Y, CAO Z, MIGNOTTE M. On simple K4-groups[J]. J Algebra, 2002,241: 658-668.
    [12]
    WANG Y. Finite groups with some subgroups of Sylow subgroups c-supplemented[J]. J Algebra, 2000, 224(2): 467-478.
    [13]
    HELIEL A A. A note on c-supplemented subgroups of finite groups[J]. Comm Algebra, 2014, 42: 1650-1656.
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    [1]
    DOERK K, HAWKES T. Finite Soluble Groups[M]. Berlin/ New York: Walter de Gruyter, 1992.
    [2]
    HUPPERT B, BLACKBURN N. Finite Groups Ⅲ[M]. Berlin/ New York: Springer-Verlag, 1982.
    [3]
    HALL P. A characteristic property of solvable groups[J]. J London Math Soc,1937,12: 188-200.
    [4]
    ARAD Z, WARD M B. New criteria for the solvability of finite groups[J]. J Algebra, 1982, 77: 234-246.
    [5]
    BALLESTER-BOLINCHES A, GUO X. On complemented subgroups of finite groups[J]. Arch Math, 1999, 72: 161-166.
    [6]
    QIAN G, TANG F. Finite groups with certain subgroups of prime power order complemented[J]. J Algebra, 2015, 423: 950-962.
    [7]
    MONAKHOV V S, KNIAHINA V N. Finite groups with complemented subgroups of prime orders[J]. J Group Theory, 2015, 18: 905-912.
    [8]
    ASAAD M. Finite groups with certain subgroups of Sylow subgroups complemented[J]. J Algebra, 2010, 323: 1958-1965.
    [9]
    GURALNICK R. Subgroups of prime power index in a simple group[J]. J Algebra, 1983, 811: 304-311.
    [10]
    GUO W. The Theory of Classes of Groups[M]. Beijing/ New York/ Dordrecht/ Boston/ London: Science Press/ Kluwer Academic Publishers, 2000.
    [11]
    BUGEAUD Y, CAO Z, MIGNOTTE M. On simple K4-groups[J]. J Algebra, 2002,241: 658-668.
    [12]
    WANG Y. Finite groups with some subgroups of Sylow subgroups c-supplemented[J]. J Algebra, 2000, 224(2): 467-478.
    [13]
    HELIEL A A. A note on c-supplemented subgroups of finite groups[J]. Comm Algebra, 2014, 42: 1650-1656.
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