Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2017.148.152hq-supplemented Subgroups of a Finite Group]]>MohamedM. Ezzat Al-ShomraniMohammed M. ElashiryM.I. 32017173Background and Objective: 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 𝔍hp-supplemented in G if G has a quasinormal subgroup N such that HN is a Hall subgroup of N and (H∩N)HG/HG<Z𝔍(G/HG), where HG is the core of H in G and Z𝔍(G/HG) is the hypercenter of G/HG. The main objective of this study is to study the structure of a finite group under the assumption that some subgroups of prime power order are 𝔍hp-supplemented in the group. Methodology: This study can improve previous results by studying the properties of the concept of 𝔍hq-supplemented and using some lemmas on these concept. Results: Results clearly reveal the influence the concept of 𝔍hq-supplemented of some subgroups of prime power order on the group. Conclusion: This study improves and extends some results of super solvability of the group by using the concept of 𝔍hq-supplemented.]]>Doerk, K. and T. Hawkes,1992Guo, W.,2000Wang, Y.,1996180954965Guo, W., X. Feng and J. Huang,201134575589Gue, W.,2008127139150Mohamed, E.M., M.I. Elashiry and M.M. Al-Shomrani,2015hq-supplemented subgroups on the structure of finite groups.]]>22261271Elkholy, A.M. and M.H. Abd El-Latif,201457277282Mohamed, M.E. and M.I. Elashiry,20164444384449Mohamed, M.E. and M.M. Alshomrani,201438658663Li, Y. and X. Zhong,2014∗-subgroups.]]>124501509Srinivasan, S.,198035210214Asaad, M.,19751837Huppert, B.,1979Vol. 1,Ramadan, M., M.E. Mohamed and A.A. Heliel,200585203210