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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 - Sayı: 2

On some second maximal subgroups of non-solvable groups

Yuyun WANG
Long MİAO
Wei LİU
Sayfa
367–373
Yayın Tarihi
2023-03-31
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 $S_{p}'$.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We call a group $G$ belongs to the class of groups $S_{p}'$, if for every $pd$-chief factor $A/B$ of $G$, $((A/B)_{p})'=1$.
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Temel Bulgular & Veri:We call a group $G$ belongs to the class of groups $S_{p}'$, if for every $pd$-chief factor $A/B$ of $G$, $((A/B)_{p})'=1$.
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Sonuç & Katkı: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 $S_{p}'$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:second maximal subgroups · maximal subgroups · simple groups

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 $S_{p}'$.

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Bu Makaleye Atıf Yap

WANG, Y., MİAO, L., LİU, W. (2023). On some second maximal subgroups of non-solvable groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 - Sayı: 2, 367–373. https://ajindex.com/articles/886286

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Kaynakça (16)

  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.