Abstract
A subgroup H of a finite group G is quasinormal in G if it permutes with every subgroup of G. A subgroup H of a finite group G is \(\mathfrak {F}_{hq}\)-supplemented in G if G has a quasinormal subgroup N such that HN is a Hall subgroup of G and \((H\cap N)H_{G}/ H_{G} \le Z_{\mathfrak {F}}(G/H_{G})\), where \(H_{G}\) is the core of H in G and \({Z}_{\mathfrak {F}} (G/H_{G})\) is the \(\mathfrak {F}\)-hypercenter of \({G/H}_{G}\). This paper concerns the structure of a finite group G under the assumption that some subgroups of G are \(\mathfrak {F}_{hq}\)-supplemented in G.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Asaad, On the supersolvability of finite groups I. Ann. Univ. Sci. Sec. Math. Bp. 18, 3–7 (1975)
K. Doerk, T. Hawkes, Finite Soluble Groups (Walter De Gruyter, Berlin, 1992)
M. Ezzat Mohamed, M.I. Elashiry, M.M. Al-Shomrani, The influence of \(\mathfrak{F}_{hq}\)-supplemented subgroups on the structure of finite groups. Wulfenia J. 22(3), 261–271 (2015)
W. Guo, The Theory of Classes of Groups (Science Press, Beijing, 2000)
W. Guo, On \(\mathfrak{F}\)-supplemented subgroups of finite groups. Manuscripta Math. 127(2), 139–150 (2008)
W. Guo, X. Feng, J. Huang, New characterizations of some classes of finite groups. Bull. Malays. Math. Sci. Soc. 34(3), 575–589 (2011)
B. Huppert, Endliche Gruppen I (Springer, Berlin, 1967)
M. Ramadan, M. Ezzat Mohamed, A.A. Heliel, On \(c\)-normality of certain subgroups of prime power order of finite groups. Arch. Math. 85, 203–210 (2005)
S. Srinivasan, Two sufficient conditions for supersolvability of finite groups. Isr. J. Math. 35, 210–214 (1980)
Y. Wang, \(C\)-normality of groups and its properties. J. Algebra 180, 954–965 (1996)
M. Weinstein, Between Nilpotent and Solvable (Polygonal Publishing House, Washington, D.C., 1982)
Acknowledgements
This paper was supported by the Deanship of Scientific Research of Northern Border University under Grant 8-19-1436-5. The authors gratefully thank the Referee for the constructive comments and suggestions which definitely helped improve the readability and quality of the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mohamed, M.E., Al-Shomrani, M.M. & Elashiry, M.I. On \(\mathfrak {F}_{hq}\)-supplemented subgroups of a finite group. Period Math Hung 76, 265–270 (2018). https://doi.org/10.1007/s10998-017-0234-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10998-017-0234-8