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Some new criteria on p-supersolubility of finite groups

  • College of Applied Mathematics, Chengdu University of Information and Technology, Chengdu 610225, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.09.005
  • Received Date: 15 January 2014
  • Accepted Date: 08 May 2014
  • Rev Recd Date: 08 May 2014
  • Publish Date: 30 September 2015
    Abstract

  • Abstract

    A subgroup H of a group G is called n-embedded in G if there exists a normal subgroup T of G，such that HT=HG and H∩T≤HsG, where HsG is the maximum s-quasinormal subgroup of G contained in H. Here, some new criteria on p-supersolubility of finite groups are obtained by n-embedded property of some subgroups.

    Abstract

    A subgroup H of a group G is called n-embedded in G if there exists a normal subgroup T of G，such that HT=HG and H∩T≤HsG, where HsG is the maximum s-quasinormal subgroup of G contained in H. Here, some new criteria on p-supersolubility of finite groups are obtained by n-embedded property of some subgroups.
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    • References(10)
  • [1]
    Guo W. The Theory of Classes of Groups [M]. Beijing/ New York: Science Press/ Kluwer, 2000.
    [2]
    徐明曜. 有限群导引[M]. 北京:科学出版社,1999.
    [3]
    Ore O. Contributions in the theory of groups of finite order[J]. Duke Math J, 1939, 5: 431-460.
    [4]
    Kegel O. Sylow-gruppen and subnormalteiler endlicher gruppen[J]. Math Z, 1962, 87: 205-221.
    [5]
    Deskins W. On quasinormal subgroups of finite groups[J]. Math Z, 1963, 82: 125-132.
    [6]
    Skiba A N. On weakly s-permutable subgroups of finite groups[J]. J Algebra, 2007, 315: 192-209.
    [7]
    Guo W, Shum K P, Skiba A N. X-semipermutable subgroups of finite groups[J]. J Algebra, 2007, 315: 31-41.
    [8]
    Li B. On Π-property and Π-normality of subgroups of finite groups[J]. J Algebra, 2011, 334: 321-337.
    [9]
    Guo W, Skiba A. Finite groups with given s-embedded and n-embedded subgroups[J]. Journal of Algebra, 2009, 321: 2 843-2 860.
    [10]
    Xie Fengyan, Li Baojun, Luo Gongzhi. Two sufficient conditions for supersovability of finite groups[J]. Journal of Xuzhou Normal University (Natural Science Edition), 2008，26（4）：8-10.
    谢凤燕，李保军，骆公志.超可解的两个判别准则[J]. 徐州师范大学学报，2008，26（4）：8-10.
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    [1]
    Guo W. The Theory of Classes of Groups [M]. Beijing/ New York: Science Press/ Kluwer, 2000.
    [2]
    徐明曜. 有限群导引[M]. 北京:科学出版社,1999.
    [3]
    Ore O. Contributions in the theory of groups of finite order[J]. Duke Math J, 1939, 5: 431-460.
    [4]
    Kegel O. Sylow-gruppen and subnormalteiler endlicher gruppen[J]. Math Z, 1962, 87: 205-221.
    [5]
    Deskins W. On quasinormal subgroups of finite groups[J]. Math Z, 1963, 82: 125-132.
    [6]
    Skiba A N. On weakly s-permutable subgroups of finite groups[J]. J Algebra, 2007, 315: 192-209.
    [7]
    Guo W, Shum K P, Skiba A N. X-semipermutable subgroups of finite groups[J]. J Algebra, 2007, 315: 31-41.
    [8]
    Li B. On Π-property and Π-normality of subgroups of finite groups[J]. J Algebra, 2011, 334: 321-337.
    [9]
    Guo W, Skiba A. Finite groups with given s-embedded and n-embedded subgroups[J]. Journal of Algebra, 2009, 321: 2 843-2 860.
    [10]
    Xie Fengyan, Li Baojun, Luo Gongzhi. Two sufficient conditions for supersovability of finite groups[J]. Journal of Xuzhou Normal University (Natural Science Edition), 2008，26（4）：8-10.
    谢凤燕，李保军，骆公志.超可解的两个判别准则[J]. 徐州师范大学学报，2008，26（4）：8-10.
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