Finite groups with some ss-quasinormal and c-normal subgroups

Abstract

Let ℱ be a saturated formation containing the class of supersolvable groups. In this paper, we use c-normal subgroups and ss-quasinormal subgroups to give criteria for a group to belong to ℱ.

Keywords

ss-quasinormal subgroup / c-normal subgroup / p-nilpotent group / saturated formation

References

[1] Deskins W. E. On quasinormal subgroups of finite groups. Mathematische Zeitschrift, 1963, 82: 125-132.

[2] Guo X. Y., Shum K. P. On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups. Archiv Der Mathematik, 2003, 80: 561-569.

[3] Huppert B. Endliche Gruppen I, 1967, Berlin, Heidelberg, New York: Springer-Verlag.

[4] Kegel O. H. Sylow gruppen and subnormalteiler endlicher gruppen. Mathematische Zeitschrift, 1962, 78: 205-221.

[5] Li D. Y., Guo X. Y. The influence of c-normality of subgroups on structure of finite groups. Communications in Algebra, 1998, 26(6): 1913-1922.

[6] Li D. Y., Guo X. Y. The influence of c-normality of subgroups on structure of finite groups. Journal of Pure and Applied Algebra, 2000, 150: 53-60.

[7] Li S. R., Shen Z. C., Kong X. H. On SS-quasinorma subgroups of finite groups. Communications in Algebra, 2008, 36: 4436-4447.

[8] Li S. R., Shen Z. C., Liu J. J., Liu X. C. The influence of SS-quasinormality of some subgroups on structure of finite groups. Journal of Algebra, 2008, 319: 4275-4287.

[9] Schmid P. Subgroups permutable with all Sylow subgroups. Journal of Algebra, 1998, 207: 285-293.

[10] Wang Y. M. C-normality of groups and its properties. Journal of Algebra, 1996, 180: 954-965.

[11] Wei H. Q. On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups. Communications in Algebra, 2001, 29(5): 21-93.

[12] Wei H. Q., Wang Y. M., Li Y. M. On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups II. Communications in Algebra, 2003, 31(10): 4807-4816.

[13] Xu M. Y. An Introduction to Finite Groups, 2001, Beijing: Science Press.