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On some second maximal subgroups of non-solvable groups

Year 2023, Volume: 52 Issue: 2, 367 - 373, 31.03.2023
https://doi.org/10.15672/hujms.1106486

Abstract

We call a group $G$ belongs to the class of groups $S_{p}'$, if for every $pd$-chief factor $A/B$ of $G$, $((A/B)_{p})'=1$. In this paper, we investigate the influence of some second maximal subgroups which are related to non-$c_{p}$-normal maximal subgroups on the structure of $S_{p}'$.

Supporting Institution

NSFC, NSFC-RFBR

Project Number

Grant \# 11871062,Grant \# 12011530061

References

  • [1] A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer, Netherlands, 2006.
  • [2] M. Bianchi, A. G. B. Mauri and P. Hauck, On finite groups with nilpotent Sylownormalizers, Arch. Math. 47 (3), 193-197, 1986.
  • [3] J. Cao, X. Guo and K. P. Shum, Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal, Comm. Algebra 46 (1), 325-334, 2018.
  • [4] W. Guo, The Theory of Classes of Groups, Science Press-Kluwer AcademicPublishers, Beijing-New York-Dordrecht-Boston-London, 2000.
  • [5] X. Guo and K. P. Shum, Cover-avoidance properties and the structure of finite groups, J. Pure Appl. Algebra 181 (2-3), 297-308, 2003.
  • [6] Z. Gao, J. Li and L. Miao, On $CAP_{S_p^*}$-subgroups of finite groups, Comm. Algebra 49 (3), 1120-1127, 2021.
  • [7] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, New York, 1967.
  • [8] B. Huppert, Normalteiler und maximale untergruppen endlichen gruppen, Math. Z. 60, 409-434, 1954.
  • [9] L. Jafari, S. Kohl and M. Zarrin, A classification of the finite non-solvable minimal non-CA-groups, J. Algebra Appl. https://doi.org/10.1142/S0219498821502030, 2021.
  • [10] Y. Lv and Y. Li, On $c_{p}$-normal subgroups of finite groups, Comm. Algebra 49 (4), 1405-1414, 2021.
  • [11] S. Li, H. Liu and D. Liu, The solvability between finite groups and semi-subnormalcover- avoidance subgroups, J. Math. 37 (6), 1303-1308, 2017.
  • [12] M. N. Konovalova, V. S. Monakhov and I. L. Sokhor, On 2-maximal subgroups of finite groups, Comm. Algebra 50 (1), 96-103, 2022.
  • [13] N. Su, C. Cao and S. Qiao, A note on maximal subgroups of $\sigma$-soluble groups, Comm. Algebra 50 (4), 1580-1584, 2022.
  • [14] J. Tate, Nilpotent quotient groups, Topology 3 (suppl. 1), 109-111, 1964.
  • [15] Y. Wang, C-normality of groups and its properties, J. Algebra 180 (3), 954-965, 1996.
  • [16] Y. Wang, L. Miao, Z. Gao and W. Liu, The influence of second maximal subgroups on the generalized p-solvability of finite groups, Comm. Algebra 50 (6), 2584-2591, 2021.
Year 2023, Volume: 52 Issue: 2, 367 - 373, 31.03.2023
https://doi.org/10.15672/hujms.1106486

Abstract

Project Number

Grant \# 11871062,Grant \# 12011530061

References

  • [1] A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer, Netherlands, 2006.
  • [2] M. Bianchi, A. G. B. Mauri and P. Hauck, On finite groups with nilpotent Sylownormalizers, Arch. Math. 47 (3), 193-197, 1986.
  • [3] J. Cao, X. Guo and K. P. Shum, Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal, Comm. Algebra 46 (1), 325-334, 2018.
  • [4] W. Guo, The Theory of Classes of Groups, Science Press-Kluwer AcademicPublishers, Beijing-New York-Dordrecht-Boston-London, 2000.
  • [5] X. Guo and K. P. Shum, Cover-avoidance properties and the structure of finite groups, J. Pure Appl. Algebra 181 (2-3), 297-308, 2003.
  • [6] Z. Gao, J. Li and L. Miao, On $CAP_{S_p^*}$-subgroups of finite groups, Comm. Algebra 49 (3), 1120-1127, 2021.
  • [7] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin, New York, 1967.
  • [8] B. Huppert, Normalteiler und maximale untergruppen endlichen gruppen, Math. Z. 60, 409-434, 1954.
  • [9] L. Jafari, S. Kohl and M. Zarrin, A classification of the finite non-solvable minimal non-CA-groups, J. Algebra Appl. https://doi.org/10.1142/S0219498821502030, 2021.
  • [10] Y. Lv and Y. Li, On $c_{p}$-normal subgroups of finite groups, Comm. Algebra 49 (4), 1405-1414, 2021.
  • [11] S. Li, H. Liu and D. Liu, The solvability between finite groups and semi-subnormalcover- avoidance subgroups, J. Math. 37 (6), 1303-1308, 2017.
  • [12] M. N. Konovalova, V. S. Monakhov and I. L. Sokhor, On 2-maximal subgroups of finite groups, Comm. Algebra 50 (1), 96-103, 2022.
  • [13] N. Su, C. Cao and S. Qiao, A note on maximal subgroups of $\sigma$-soluble groups, Comm. Algebra 50 (4), 1580-1584, 2022.
  • [14] J. Tate, Nilpotent quotient groups, Topology 3 (suppl. 1), 109-111, 1964.
  • [15] Y. Wang, C-normality of groups and its properties, J. Algebra 180 (3), 954-965, 1996.
  • [16] Y. Wang, L. Miao, Z. Gao and W. Liu, The influence of second maximal subgroups on the generalized p-solvability of finite groups, Comm. Algebra 50 (6), 2584-2591, 2021.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Yuyun Wang This is me 0000-0002-0145-929X

Long Miao This is me 0000-0001-5286-3690

Wei Liu 0000-0003-0080-8133

Project Number Grant \# 11871062,Grant \# 12011530061
Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 52 Issue: 2

Cite

APA Wang, Y., Miao, L., & Liu, W. (2023). On some second maximal subgroups of non-solvable groups. Hacettepe Journal of Mathematics and Statistics, 52(2), 367-373. https://doi.org/10.15672/hujms.1106486
AMA Wang Y, Miao L, Liu W. On some second maximal subgroups of non-solvable groups. Hacettepe Journal of Mathematics and Statistics. March 2023;52(2):367-373. doi:10.15672/hujms.1106486
Chicago Wang, Yuyun, Long Miao, and Wei Liu. “On Some Second Maximal Subgroups of Non-Solvable Groups”. Hacettepe Journal of Mathematics and Statistics 52, no. 2 (March 2023): 367-73. https://doi.org/10.15672/hujms.1106486.
EndNote Wang Y, Miao L, Liu W (March 1, 2023) On some second maximal subgroups of non-solvable groups. Hacettepe Journal of Mathematics and Statistics 52 2 367–373.
IEEE Y. Wang, L. Miao, and W. Liu, “On some second maximal subgroups of non-solvable groups”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, pp. 367–373, 2023, doi: 10.15672/hujms.1106486.
ISNAD Wang, Yuyun et al. “On Some Second Maximal Subgroups of Non-Solvable Groups”. Hacettepe Journal of Mathematics and Statistics 52/2 (March 2023), 367-373. https://doi.org/10.15672/hujms.1106486.
JAMA Wang Y, Miao L, Liu W. On some second maximal subgroups of non-solvable groups. Hacettepe Journal of Mathematics and Statistics. 2023;52:367–373.
MLA Wang, Yuyun et al. “On Some Second Maximal Subgroups of Non-Solvable Groups”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, 2023, pp. 367-73, doi:10.15672/hujms.1106486.
Vancouver Wang Y, Miao L, Liu W. On some second maximal subgroups of non-solvable groups. Hacettepe Journal of Mathematics and Statistics. 2023;52(2):367-73.