On the semi cover-avoiding property and $\mathcal{F}$-supplementation

Document Type: Research Paper

Authors

xuzhou normal university

Abstract

In this paper‎, ‎we investigate the influence of some subgroups of Sylow subgroups with semi cover-avoiding property and‎ ‎$\mathcal{F}$-supplementation on the structure of finite groups and generalize a series of known results‎.

Keywords

Main Subjects


A. Y. AlsheikAhmad, J. J. Jaraden and A. N. Skiba (2007). On $mathcal{U}_{c}$-normal subgroups of finite groups. Algebra Colloq.. 14, 25-36
A. Ballester-Bolinches and X. Guo (1999). On complemented subgroups of finite groups. Arch. Math.. 72, 161-166
L. M. Ezquerro (1993). A contribution to the theory of finite supersolvable groups. Rend. Sem. Mat. Univ. Padova,. 89, 161-170
Y. Fan, X. Guo and K. P. Shum (2006). Remarks on two generalizations of normality of subgroups. Chinese Ann. Math. A,. 27, 169-176
W. Gasch"{u}tz (1963). Praefrattinigruppen. Arch. Math.. 13
J. D. Gillam (1974). Cover-avoid subgroups in finite solvable groups. J. Algebra,. 29, 324-329
F. Gross (1987). Conjugacy of odd order Hall subgroups. Bull. London Math. Soc.. 19, 311-319
W. Guo (2008). On $mathcal{F}$-supplemented subgroups of finite groups. Manuscripta Math.. 127, 139-150
X. Guo, P. Guo and K. P. Shum (2007). On semi cover-avoiding subgroups of finite group. J. Pure Appl. Algebra,. 209, 151-158
X. Guo and K. P. Shum (2003). Cover-avoidance properties and the structure of finite groups. J. Pure Appl. Algebra,. 181, 297-308
X. Guo and K. P. Shum (2003). On $c$-normal maximal and minimal subgroups of Sylow $p$-subgroups of finite groups. Arch. Math.. 80, 561-569
X. Guo and K. P. Shum (2005). Finite $p$-nilpotent groups with some subgroups $c$-supplemented. J. Aust. Math. Soc.. 78, 429-439
X. Guo and K. P. Shum (2003). On $p$-nilpotency of finite groups with some subgroups $c$-supplemented. Algebra Colloq.. 10, 259-266
X. Guo and K. P. Shum (2006). Complementarity of subgroups and the structure of finite groups. Algebra Colloq.. 13, 9-16
X. Guo and L. Wang (2007). On finite groups with some semi cover-avoiding subgroups. Acta Math. Sin.. 23, 1689-1696
X. Guo, J. Wang and K. P. Shum (2006). On semi cover-avoiding maximal subgroup and solvability of finite groups. Comm. Algebra,. 34, 3235-3244
B. Huppert (1967). Endliche Gruppen I,. Springer-Verlag, Berlin-New York.
D. Li and X. Guo (2000). The influence of $c$-normality of subgroups on the structure of finite groups. J. Pure Appl. Algebra,. 150, 53-60
X. Li and Y. Yang (2008). Semi $CAP$-subgroups and the structure of finite groups. Acta Math. Sin.. 51, 1181-1187
A. N. Skiba (2007). On weakly $s$-permutable subgroups of finite groups. J. Algebra,. 315, 192-209
Y. Wang (2000). Finite groups with some subgroups of Sylow subgroups $c$-supplemented. J. Algebra,. 224, 467-478
Y. Wang (1996). $c$-Normality of groups and its properties. J. Algebra,. 180, 954-965
Y. Wang and H. Wei (2004). On a problem of Skiba from the Kourovka Notebook. Sci. China Ser. A,. 47, 96-103
Y. Wang, H. Wei and Y. Li (2002). A generalization of Kramer's theorem and its application. Bull. Aust. Math. Soc.. 65, 467-475
H. Wei (2001). On $c$-normal maximal and minimal subgroups of Sylow subgroups of finite groups. Comm. Algebra,. 29, 2193-2200
H. Wei and Y. Wang (2007). On $c^{ast}$-normality and its properties. J. Group Theory,. 10, 211-223
T. Zhao and X. Li (2010). Semi cover-avoiding properties of finite groups. Front. Math. China,. 5, 79-800