Finite groups with some $SS$-embedded subgroups

Document Type: Research Paper


School of Science, Shandong University of Technology


We call $H$ an $SS$-embedded subgroup of $G$ if there exists a‎ ‎normal subgroup $T$ of $G$ such that $HT$ is subnormal in $G$ and‎ ‎$H\cap T\leq H_{sG}$‎, ‎where $H_{sG}$ is the maximal $s$-permutable‎ ‎subgroup of $G$ contained in $H$‎. ‎In this paper‎, ‎we investigate the‎ ‎influence of some $SS$-embedded subgroups on the structure of a‎ ‎finite group $G$‎. ‎Some new results were obtained.‎


Main Subjects

W. E. Deskins (1963). On quasinormal subgroups of finite groups. Math. Z.. 82, 125-132
D. Gorenstein (1968). Finite Groups. Chelsea Publishing Company, New York.
W. B. Guo, K. P. Shum and A. N. Skiba (2009). On solubility and supersolubility of some classes of finite groups. Sci. China (Ser. A). 52, 272-286
W. B. Guo, K. P. Shum and F. Y. Xie (2011). Finite groups with some weakly $s$-supplemented subgroups. Glasg. Math. J.. 53, 211-222
W. B. Guo, Y. Wang and L. Shi (2008). Nearly $s$-normal subgroups of a finite group. J. Algebra Discrete Struct.. 6, 95-106
B. Huppert (1967). Endliche Gruppen Vol. I. Springer, New York.
O. H. Kegel (1962). Sylow-Gruppen und abnormalteiler endlicher Gruppen. Math. Z.. 78, 205-221
I. A. Malinowska (2012). Finite groups with $sn$-embedded or $s$-embedded subgroups. Acta Math. Hungar.. 136, 76-89
D. J. S. Robinson (1993). A Course in the Theory of Group. Springer-Verlag, New York-Berlin.
A. N. Skiba (2007). On weakly $s$-permutable subgroups of finite groups. J. Algebra. 315, 192-209
Y. M. Wang (1996). $C$-normality of groups and its properties. J. Algebra. 180, 954-965
Y. M. Wang (1996). $C$-normality and solvability of groups. J. Pure Appl. Algebra. 110, 315-320
Y. Wang and W. B. Guo (2010). Nearly $s$-normality of groups and its properties. Comm. Algebra. 38, 3821-3836