Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 52 Sayı: 2, 420 - 425, 31.03.2023
https://doi.org/10.15672/hujms.1114323

Öz

Proje Numarası

No. 12071181

Kaynakça

  • [1] R.K. Agrawal, Finite groups whose subnormal subgroups permute with all Sylow subgroups, Proc. Amer. Math. Soc. 47 (1), 77–83, 1975.
  • [2] A. Beltrán, On powers of conjugacy classes in a finite group, J. Group Theory 25 (5), 965–971, 2022.
  • [3] A. Beltrán and M.J. Felipe, Cosets of normal subgroups and powers of conjugacy classes, Math. Nachr. 294, 1652–1656, 2021.
  • [4] J.D. Dixon and B. Mortimer, Permutation Groups, Springer-Verlag, New York, 1996.
  • [5] B. Huppert, Endliche Gruppen, Springer-Verlag, Berlin, Heidelberg, New York, 1967.
  • [6] Q. Jiang and C. Shao, Primary and biprimary class sizes implying nilpotency of finite groups, Turkish J. Math. 40 (2), 389–396, 2016.
  • [7] O.H. Kegel, Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z. 78, 205–221, 1962.
  • [8] S. Li, Z. Shen, J. Liu and X. Liu, The influence of SS-quasinormality of some subgroups on the structure of finite groups, J. Algebra 319, 4275–4287, 2008.
  • [9] D.J.S. Robinson, A Course in the Theory of Groups, Springer-Verlag, New York, 1996.
  • [10] C. Shao and Q. Jiang, Finite groups with three conjugacy class sizes of primary and biprimary elements, Turkish J. Math. 39 (3), 346–355, 2015.
  • [11] S. Srinivasan, Two sufficient conditions for supersolvability of finite groups, Israel J. Math. 35, 210–214, 1980.
  • [12] J.G. Thompson, Normal p-complements for finite groups, Math. Z. 72, 332–354, 1959/1960.
  • [13] J.G. Thompson, Normal p-complements for finite groups, J. Algebra 1, 43–46, 1964.
  • [14] J.G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74, 383–437, 1968.

A constructive approach: From local subgroups to new classes of finite groups

Yıl 2023, Cilt: 52 Sayı: 2, 420 - 425, 31.03.2023
https://doi.org/10.15672/hujms.1114323

Öz

Let G be a finite group and S be a proper subgroup of G. A group G is called an S-(S-quasinormal)-group if every local subgroup of G is either an S-quasinormal subgroup or conjugate to a subgroup of S. The main purpose of this construction is to demonstrate a new way of analyzing the structure of a finite group by the properties and the number of conjugacy classes of its local subgroups.

Destekleyen Kurum

Natural Science Foundation of China

Proje Numarası

No. 12071181

Kaynakça

  • [1] R.K. Agrawal, Finite groups whose subnormal subgroups permute with all Sylow subgroups, Proc. Amer. Math. Soc. 47 (1), 77–83, 1975.
  • [2] A. Beltrán, On powers of conjugacy classes in a finite group, J. Group Theory 25 (5), 965–971, 2022.
  • [3] A. Beltrán and M.J. Felipe, Cosets of normal subgroups and powers of conjugacy classes, Math. Nachr. 294, 1652–1656, 2021.
  • [4] J.D. Dixon and B. Mortimer, Permutation Groups, Springer-Verlag, New York, 1996.
  • [5] B. Huppert, Endliche Gruppen, Springer-Verlag, Berlin, Heidelberg, New York, 1967.
  • [6] Q. Jiang and C. Shao, Primary and biprimary class sizes implying nilpotency of finite groups, Turkish J. Math. 40 (2), 389–396, 2016.
  • [7] O.H. Kegel, Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z. 78, 205–221, 1962.
  • [8] S. Li, Z. Shen, J. Liu and X. Liu, The influence of SS-quasinormality of some subgroups on the structure of finite groups, J. Algebra 319, 4275–4287, 2008.
  • [9] D.J.S. Robinson, A Course in the Theory of Groups, Springer-Verlag, New York, 1996.
  • [10] C. Shao and Q. Jiang, Finite groups with three conjugacy class sizes of primary and biprimary elements, Turkish J. Math. 39 (3), 346–355, 2015.
  • [11] S. Srinivasan, Two sufficient conditions for supersolvability of finite groups, Israel J. Math. 35, 210–214, 1980.
  • [12] J.G. Thompson, Normal p-complements for finite groups, Math. Z. 72, 332–354, 1959/1960.
  • [13] J.G. Thompson, Normal p-complements for finite groups, J. Algebra 1, 43–46, 1964.
  • [14] J.G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74, 383–437, 1968.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Zhencai Shen 0000-0001-5423-4126

Baoyu Zhang 0000-0001-7716-8547

Haonan Jıang 0000-0002-6457-6020

Proje Numarası No. 12071181
Yayımlanma Tarihi 31 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 2

Kaynak Göster

APA Shen, Z., Zhang, B., & Jıang, H. (2023). A constructive approach: From local subgroups to new classes of finite groups. Hacettepe Journal of Mathematics and Statistics, 52(2), 420-425. https://doi.org/10.15672/hujms.1114323
AMA Shen Z, Zhang B, Jıang H. A constructive approach: From local subgroups to new classes of finite groups. Hacettepe Journal of Mathematics and Statistics. Mart 2023;52(2):420-425. doi:10.15672/hujms.1114323
Chicago Shen, Zhencai, Baoyu Zhang, ve Haonan Jıang. “A Constructive Approach: From Local Subgroups to New Classes of Finite Groups”. Hacettepe Journal of Mathematics and Statistics 52, sy. 2 (Mart 2023): 420-25. https://doi.org/10.15672/hujms.1114323.
EndNote Shen Z, Zhang B, Jıang H (01 Mart 2023) A constructive approach: From local subgroups to new classes of finite groups. Hacettepe Journal of Mathematics and Statistics 52 2 420–425.
IEEE Z. Shen, B. Zhang, ve H. Jıang, “A constructive approach: From local subgroups to new classes of finite groups”, Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 2, ss. 420–425, 2023, doi: 10.15672/hujms.1114323.
ISNAD Shen, Zhencai vd. “A Constructive Approach: From Local Subgroups to New Classes of Finite Groups”. Hacettepe Journal of Mathematics and Statistics 52/2 (Mart 2023), 420-425. https://doi.org/10.15672/hujms.1114323.
JAMA Shen Z, Zhang B, Jıang H. A constructive approach: From local subgroups to new classes of finite groups. Hacettepe Journal of Mathematics and Statistics. 2023;52:420–425.
MLA Shen, Zhencai vd. “A Constructive Approach: From Local Subgroups to New Classes of Finite Groups”. Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 2, 2023, ss. 420-5, doi:10.15672/hujms.1114323.
Vancouver Shen Z, Zhang B, Jıang H. A constructive approach: From local subgroups to new classes of finite groups. Hacettepe Journal of Mathematics and Statistics. 2023;52(2):420-5.