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Open AccessOpen Access JUSTC Mathematics 14 June 2023

New criteria of supersolubility of finite groups

  • 1.

    School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China

  • 2.

    Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Cite this:
https://doi.org/10.52396/JUSTC-2022-0132
More Information
  • Author Bio:

    Xueli Yang is currently a postgraduate student at Ningbo University. Her research mainly focuses on the theory of finite groups

    Chenchen Cao is currently a Lecture at Ningbo University. He received his Ph.D. degree in Mathematics from the University of Science and Technology of China in 2019. His research mainly focuses on the strcture of finite groups

  • Corresponding author: E-mail: caochenchen@nbu.edu.cn
  • Received Date: 17 September 2022
  • Accepted Date: 12 December 2022
    • Available Online: 14 June 2023
    Abstract

  • Abstract

    We study the structure of finite groups in which some given subgroups are $\sigma$-embedded. In particular, we obtain some new criteria for the supersolubility of finite groups, which generalize some known results.

    Graphical abstract

    Some new criteria of supersolubility of finite groups are obtained by assuming that some given subgroups are σ-embedded.

    Abstract

    We study the structure of finite groups in which some given subgroups are $\sigma$-embedded. In particular, we obtain some new criteria for the supersolubility of finite groups, which generalize some known results.

    • Public Summary

    • Some new properties of σ-embedded subgroups are established.
    • Some new criteria of supersolubility of finite groups are obtained.
    • Some known results in this research field are generalized.

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    • References(20)
  • [1]
    Guo W, Skiba A N. On $ \Pi $ -permutable subgroups of finite groups. Monatsh. Math., 2018, 185 (3): 443–453. doi: 10.1007/s00605-016-1007-9
    [2]
    Skiba A N. On σ-subnormal and σ-permutable subgroups of finite groups. J. Algebra, 2015, 436: 1–16. doi: 10.1016/j.jalgebra.2015.04.010
    [3]
    Skiba A N. On some results in the theory of finite partially soluble groups. Commun. Math. Stat., 2016, 4 (3): 281–309. doi: 10.1007/s40304-016-0088-z
    [4]
    Zhang C, Guo W, Liu A-M. On a generalization of finite T-groups. Commun. Math. Stat., 2022, 10: 153–162. doi: 10.1007/s40304-021-00240-z
    [5]
    Wang Y. C-Normality of groups and its properties. J. Algebra, 1996, 180: 954–965. doi: 10.1006/jabr.1996.0103
    [6]
    Guo W, Skiba A N. Finite groups with given s-embedded and n-embedded subgroups. J. Algebra, 2009, 321: 2843–2860. doi: 10.1016/j.jalgebra.2009.02.016
    [7]
    Wu Z, Zhang C, Huang J. Finite groups with given σ-embedded and σ-n-embedded subgroups. Indian J. Pure Appl. Math., 2017, 48 (3): 429–448. doi: 10.1007/s13226-017-0239-2
    [8]
    Amjid V, Guo W, Li B. On σ-embedded and σ-n-embedded subgroups of finite groups. Sib. Math. J., 2019, 60: 389–397. doi: 10.1134/S0037446619030030
    [9]
    Asaad M. On the solvability of finite groups. Arch. Math., 1988, 51: 289–293. doi: 10.1007/BF01194016
    [10]
    Asaad M, Ezzat Mohamed M. On c-normality of finite groups. J. Aust. Math. Soc., 2005, 78: 297–304. doi: 10.1017/S1446788700008545
    [11]
    Ballester-Bolinches A, Wang Y. Finite groups with some c-normal minimal subgroups. J. Pure Appl. Algebra, 2000, 153: 121–127. doi: 10.1016/s0022-4049(99)00165-6
    [12]
    Li D, Guo X. The influence of c-normality of subgroups on the structure of finite groups. J. Pure Appl. Algebra, 2000, 150: 53–60. doi: 10.1016/s0022-4049(99)00042-0
    [13]
    Shaalan A. The influence of π-quasinormality of some subgroups on the structure of a finite group. Acta Math. Hung., 1990, 56: 287–293. doi: 10.1007/BF01903844
    [14]
    Ballester-Bolinches A, Esteban-Romero R, Asaad M. Products of Finite Groups. Berlin: De Gruyter, 2010.
    [15]
    Doerk K, Hawkes T. Finite Soluble Groups. Berlin: De Gruyter, 1992.
    [16]
    Guo W. Structure Theory for Canonical Classes of Finite Groups. Berlin: Springer, 2015.
    [17]
    Doerk K. Minimal nicht überauflösbare, endliche Gruppe. Math. Z., 1966, 91: 198–205. doi: 10.1007/BF01312426
    [18]
    Huppert B. Endliche Gruppen I. Berlin: Springer, 1967.
    [19]
    Skiba A N. On weakly s-permutable subgroups of finite groups. J. Algebra, 2007, 315: 192–209. doi: 10.1016/j.jalgebra.2007.04.025
    [20]
    Buckley J. Finite groups whose minimal subgroups are normal. Math. Z., 1970, 116: 15–17. doi: 10.1007/BF01110184
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    [1]
    Guo W, Skiba A N. On $ \Pi $ -permutable subgroups of finite groups. Monatsh. Math., 2018, 185 (3): 443–453. doi: 10.1007/s00605-016-1007-9
    [2]
    Skiba A N. On σ-subnormal and σ-permutable subgroups of finite groups. J. Algebra, 2015, 436: 1–16. doi: 10.1016/j.jalgebra.2015.04.010
    [3]
    Skiba A N. On some results in the theory of finite partially soluble groups. Commun. Math. Stat., 2016, 4 (3): 281–309. doi: 10.1007/s40304-016-0088-z
    [4]
    Zhang C, Guo W, Liu A-M. On a generalization of finite T-groups. Commun. Math. Stat., 2022, 10: 153–162. doi: 10.1007/s40304-021-00240-z
    [5]
    Wang Y. C-Normality of groups and its properties. J. Algebra, 1996, 180: 954–965. doi: 10.1006/jabr.1996.0103
    [6]
    Guo W, Skiba A N. Finite groups with given s-embedded and n-embedded subgroups. J. Algebra, 2009, 321: 2843–2860. doi: 10.1016/j.jalgebra.2009.02.016
    [7]
    Wu Z, Zhang C, Huang J. Finite groups with given σ-embedded and σ-n-embedded subgroups. Indian J. Pure Appl. Math., 2017, 48 (3): 429–448. doi: 10.1007/s13226-017-0239-2
    [8]
    Amjid V, Guo W, Li B. On σ-embedded and σ-n-embedded subgroups of finite groups. Sib. Math. J., 2019, 60: 389–397. doi: 10.1134/S0037446619030030
    [9]
    Asaad M. On the solvability of finite groups. Arch. Math., 1988, 51: 289–293. doi: 10.1007/BF01194016
    [10]
    Asaad M, Ezzat Mohamed M. On c-normality of finite groups. J. Aust. Math. Soc., 2005, 78: 297–304. doi: 10.1017/S1446788700008545
    [11]
    Ballester-Bolinches A, Wang Y. Finite groups with some c-normal minimal subgroups. J. Pure Appl. Algebra, 2000, 153: 121–127. doi: 10.1016/s0022-4049(99)00165-6
    [12]
    Li D, Guo X. The influence of c-normality of subgroups on the structure of finite groups. J. Pure Appl. Algebra, 2000, 150: 53–60. doi: 10.1016/s0022-4049(99)00042-0
    [13]
    Shaalan A. The influence of π-quasinormality of some subgroups on the structure of a finite group. Acta Math. Hung., 1990, 56: 287–293. doi: 10.1007/BF01903844
    [14]
    Ballester-Bolinches A, Esteban-Romero R, Asaad M. Products of Finite Groups. Berlin: De Gruyter, 2010.
    [15]
    Doerk K, Hawkes T. Finite Soluble Groups. Berlin: De Gruyter, 1992.
    [16]
    Guo W. Structure Theory for Canonical Classes of Finite Groups. Berlin: Springer, 2015.
    [17]
    Doerk K. Minimal nicht überauflösbare, endliche Gruppe. Math. Z., 1966, 91: 198–205. doi: 10.1007/BF01312426
    [18]
    Huppert B. Endliche Gruppen I. Berlin: Springer, 1967.
    [19]
    Skiba A N. On weakly s-permutable subgroups of finite groups. J. Algebra, 2007, 315: 192–209. doi: 10.1016/j.jalgebra.2007.04.025
    [20]
    Buckley J. Finite groups whose minimal subgroups are normal. Math. Z., 1970, 116: 15–17. doi: 10.1007/BF01110184
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