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.
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.
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.
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.