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A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS

Yıl 2020, Cilt: 27 Sayı: 27, 263 - 270, 07.01.2020
https://doi.org/10.24330/ieja.663084

Öz

In this paper, we find a condition under which every chief factor of $G$ below a normal subgroup $H$ of $G$ is cyclic by using the $\tau$-supplemented subgroups. Some recent results are generalized.

Kaynakça

  • A. Ballester-Bolinches, Y. Wang and G. Xiuyun, c-supplemented subgroups of finite groups, Glasg. Math. J., 42(3) (2000), 383-389.
  • K. Doerk and T. Hawkes, Finite Soluble Groups, De Gruyter Expositions in Mathematics, 4, Walter de Gruyter & Co., Berlin, 1992.
  • X. Guo and K. P. Shum, Finite p-nilpotent groups with some subgroups c- supplemented, J. Aust. Math. Soc., 78(3) (2005), 429-439.
  • B. Huppert and N. Blackburn, Finite Groups III, Fundamental Principles of Mathematical Sciences, 243, Springer-Verlag, Berlin-New York, 1982.
  • I. M. Isaacs, Semipermutable $\pi$-subgroups, Arch. Math. (Basel), 102(1) (2014), 1-6.
  • O. H. Kegel, Sylow-gruppen und subnormalteiler endlicher gruppen, Math. Z., 78(1) (1962), 205-221.
  • C. Li, Finite groups with some primary subgroups SS-quasinormally embedded, Indian J. Pure Appl. Math., 42(5) (2011), 291-306.
  • 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(10) (2008), 4275- 4287.
  • C. Li, N. Yang and N. Tang, Some new characterisations of finite p-supersoluble groups, Bull. Aust. Math. Soc., 89(3) (2014), 514-521.
  • C. Li, X. Zhang and X. Yi, On $\tau$-supplemented subgroups of finite groups, Miskolc Math. Notes, 14(3) (2013), 997-1008.
  • V. O. Lukyanenko and A. N. Skiba, On weakly $\tau$-quasinormal subgroups of finite groups, Acta Math. Hungar., 125(3) (2009), 237-248.
  • P. Schmidt, Subgroups permutable with all Sylow subgroups, J. Algebra, 207(1) (1998), 285-293.
  • A. N. Skiba, On weakly s-permutable subgroups of finite groups, J. Algebra, 315(1) (2007), 192-209.
  • A. N. Skiba, On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups, J. Group Theory, 13(6) (2010), 841-850.
  • L. Wang and Y. Wang, On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups, Comm. Algebra, 34(1) (2006), 143-149.
  • H. Wei, Y. Wang and Y. Li, On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups, Proc. Amer. Math. Soc., 132(8) (2004), 2197-2204.
  • Q. Yan, X. Bao and Z. Shen, Finite groups with SS-supplement, Monatsh. Math., 184(2) (2017), 325-333.
Yıl 2020, Cilt: 27 Sayı: 27, 263 - 270, 07.01.2020
https://doi.org/10.24330/ieja.663084

Öz

Kaynakça

  • A. Ballester-Bolinches, Y. Wang and G. Xiuyun, c-supplemented subgroups of finite groups, Glasg. Math. J., 42(3) (2000), 383-389.
  • K. Doerk and T. Hawkes, Finite Soluble Groups, De Gruyter Expositions in Mathematics, 4, Walter de Gruyter & Co., Berlin, 1992.
  • X. Guo and K. P. Shum, Finite p-nilpotent groups with some subgroups c- supplemented, J. Aust. Math. Soc., 78(3) (2005), 429-439.
  • B. Huppert and N. Blackburn, Finite Groups III, Fundamental Principles of Mathematical Sciences, 243, Springer-Verlag, Berlin-New York, 1982.
  • I. M. Isaacs, Semipermutable $\pi$-subgroups, Arch. Math. (Basel), 102(1) (2014), 1-6.
  • O. H. Kegel, Sylow-gruppen und subnormalteiler endlicher gruppen, Math. Z., 78(1) (1962), 205-221.
  • C. Li, Finite groups with some primary subgroups SS-quasinormally embedded, Indian J. Pure Appl. Math., 42(5) (2011), 291-306.
  • 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(10) (2008), 4275- 4287.
  • C. Li, N. Yang and N. Tang, Some new characterisations of finite p-supersoluble groups, Bull. Aust. Math. Soc., 89(3) (2014), 514-521.
  • C. Li, X. Zhang and X. Yi, On $\tau$-supplemented subgroups of finite groups, Miskolc Math. Notes, 14(3) (2013), 997-1008.
  • V. O. Lukyanenko and A. N. Skiba, On weakly $\tau$-quasinormal subgroups of finite groups, Acta Math. Hungar., 125(3) (2009), 237-248.
  • P. Schmidt, Subgroups permutable with all Sylow subgroups, J. Algebra, 207(1) (1998), 285-293.
  • A. N. Skiba, On weakly s-permutable subgroups of finite groups, J. Algebra, 315(1) (2007), 192-209.
  • A. N. Skiba, On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups, J. Group Theory, 13(6) (2010), 841-850.
  • L. Wang and Y. Wang, On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups, Comm. Algebra, 34(1) (2006), 143-149.
  • H. Wei, Y. Wang and Y. Li, On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups, Proc. Amer. Math. Soc., 132(8) (2004), 2197-2204.
  • Q. Yan, X. Bao and Z. Shen, Finite groups with SS-supplement, Monatsh. Math., 184(2) (2017), 325-333.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Changwen Li Bu kişi benim

Yayımlanma Tarihi 7 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 27 Sayı: 27

Kaynak Göster

APA Li, C. (2020). A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS. International Electronic Journal of Algebra, 27(27), 263-270. https://doi.org/10.24330/ieja.663084
AMA Li C. A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS. IEJA. Ocak 2020;27(27):263-270. doi:10.24330/ieja.663084
Chicago Li, Changwen. “A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS”. International Electronic Journal of Algebra 27, sy. 27 (Ocak 2020): 263-70. https://doi.org/10.24330/ieja.663084.
EndNote Li C (01 Ocak 2020) A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS. International Electronic Journal of Algebra 27 27 263–270.
IEEE C. Li, “A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS”, IEJA, c. 27, sy. 27, ss. 263–270, 2020, doi: 10.24330/ieja.663084.
ISNAD Li, Changwen. “A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS”. International Electronic Journal of Algebra 27/27 (Ocak 2020), 263-270. https://doi.org/10.24330/ieja.663084.
JAMA Li C. A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS. IEJA. 2020;27:263–270.
MLA Li, Changwen. “A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS”. International Electronic Journal of Algebra, c. 27, sy. 27, 2020, ss. 263-70, doi:10.24330/ieja.663084.
Vancouver Li C. A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS. IEJA. 2020;27(27):263-70.