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On S-c-propermutable subgroups of finite groups

  • 1.

    School of Math. and Comp. Sci., Shanxi Datong University, Datong 037009, China

  • 2.

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

  • 3.

    School of Science, Jiangnan University, Wuxi 214122, China

Funds:  Supported by an NNSF of China (11371335) and Natural Science Youth Foundation of Jiangsu Provincial (20130119).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.12.003
More Information
  • Corresponding author: MAO Yuemei (corresponding author), female, born in 1980, PhD candidate. Research field: group theory.
  • Received Date: 14 June 2015
  • Accepted Date: 10 December 2015
  • Rev Recd Date: 10 December 2015
  • Publish Date: 30 December 2015
    Abstract

  • Abstract

    A subgroup H of a group G is said to be S-c-propermutable in G if G has a subgroup B such that G=NG(H)B and for every Sylow subgroup A of B, there exists an element x∈B such that HAx=AxH. Here, S-c-propermutable subgroups were used to study the structure of finite groups and some new criteria of supersoluble groups were obtained.

    Abstract

    A subgroup H of a group G is said to be S-c-propermutable in G if G has a subgroup B such that G=NG(H)B and for every Sylow subgroup A of B, there exists an element x∈B such that HAx=AxH. Here, S-c-propermutable subgroups were used to study the structure of finite groups and some new criteria of supersoluble groups were obtained.
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    • References(13)
  • [1]
    Doerk K, Hawkes T. Finite Soluble Groups[M]. Berlin/ New York: Walter de Gruyter, 1992.
    [2]
    Guo W. The Theory of Classes of Groups[M]. Beijing/ New York: Science Press/ Kluwer Academic Publishers, 2000.
    [3]
    Huppert B.Endliche Gruppen Ⅰ[M]. New York: Springer, 1967.
    [4]
    Yi X,Skiba A N. On S-propermutable subgroups of finite groups[J]. Bull Malays Math Sci Soc, 2015, 38(2): 605-616.
    [5]
    Huang J,Guo W. The S-conditionally permutable subgroups of finite groups[J]. Chin Ann Math, 2007, 28A: 17-26.
    [6]
    Guo W. On F-supplemented subgroups of finite groups[J]. Manu Math, 2008, 127: 139-150.
    [7]
    Chen X,Guo W. On п-supplemented subgroups of finite groups[DB/OL]. arXiv: 1307.0089
    [8]
    Gorenstein D. Finite Groups[M]. New York: Chelsea, 1968.
    [9]
    Guo W, Skiba A N. Finite groups with given s-embedded and n-embedded subgroups[J]. J Algebra, 2009, 321: 2 843-2 860.
    [10]
    Skiba A N. On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups[J]. J Group Theory, 2010, 13: 841-850.
    [11]
    Su N, Li Y, Wang Y. A criterion of p-hypercyclically embedded subgroups of finite groups[J]. J Algebra, 2014, 400: 82-93.
    [12]
    Skiba A N. On weakly s-permutable subgroups of finite groups[J]. J Algebra, 2007, 315(1):192-209.
    [13]
    Du Z. Hall subgroups and п-separable groups[J]. J Algebra, 1997, 195: 501-509.
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    [1]
    Doerk K, Hawkes T. Finite Soluble Groups[M]. Berlin/ New York: Walter de Gruyter, 1992.
    [2]
    Guo W. The Theory of Classes of Groups[M]. Beijing/ New York: Science Press/ Kluwer Academic Publishers, 2000.
    [3]
    Huppert B.Endliche Gruppen Ⅰ[M]. New York: Springer, 1967.
    [4]
    Yi X,Skiba A N. On S-propermutable subgroups of finite groups[J]. Bull Malays Math Sci Soc, 2015, 38(2): 605-616.
    [5]
    Huang J,Guo W. The S-conditionally permutable subgroups of finite groups[J]. Chin Ann Math, 2007, 28A: 17-26.
    [6]
    Guo W. On F-supplemented subgroups of finite groups[J]. Manu Math, 2008, 127: 139-150.
    [7]
    Chen X,Guo W. On п-supplemented subgroups of finite groups[DB/OL]. arXiv: 1307.0089
    [8]
    Gorenstein D. Finite Groups[M]. New York: Chelsea, 1968.
    [9]
    Guo W, Skiba A N. Finite groups with given s-embedded and n-embedded subgroups[J]. J Algebra, 2009, 321: 2 843-2 860.
    [10]
    Skiba A N. On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups[J]. J Group Theory, 2010, 13: 841-850.
    [11]
    Su N, Li Y, Wang Y. A criterion of p-hypercyclically embedded subgroups of finite groups[J]. J Algebra, 2014, 400: 82-93.
    [12]
    Skiba A N. On weakly s-permutable subgroups of finite groups[J]. J Algebra, 2007, 315(1):192-209.
    [13]
    Du Z. Hall subgroups and п-separable groups[J]. J Algebra, 1997, 195: 501-509.
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