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A CONDITION FOR CYCLIC CHIEF FACTORS OF FINITE GROUPS

Year 2020, , 263 - 270, 07.01.2020
https://doi.org/10.24330/ieja.663084

Abstract

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.

References

  • 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.
Year 2020, , 263 - 270, 07.01.2020
https://doi.org/10.24330/ieja.663084

Abstract

References

  • 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.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Changwen Li This is me

Publication Date January 7, 2020
Published in Issue Year 2020

Cite

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. January 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, no. 27 (January 2020): 263-70. https://doi.org/10.24330/ieja.663084.
EndNote Li C (January 1, 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, vol. 27, no. 27, pp. 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 (January 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, vol. 27, no. 27, 2020, pp. 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.