Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2017.148.152hq-supplemented Subgroups of a Finite Group]]>MohamedM. EzzatAl-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 𝔍_{hp}-supplemented in G if G has a quasinormal subgroup N such that HN is a Hall subgroup of N and (H∩N)H_{G}/H_{G}<Z_{𝔍}(G/H_{G}), where H_{G} is the core of H in G and Z_{𝔍}(G/H_{G}) is the hypercenter of G/H_{G}. 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 𝔍_{hp}-supplemented in the group. Methodology: This study can improve previous results by studying the properties of the concept of 𝔍_{hq}-supplemented and using some lemmas on these concept. Results: Results clearly reveal the influence the concept of 𝔍_{hq}-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 𝔍_{hq}-supplemented.]]>Doerk, K. and T. Hawkes,1992Guo, W.,2000Wang, Y.,1996Guo, W., X. Feng and J. Huang,2011Gue, W.,2008Mohamed, E.M., M.I. Elashiry and M.M. Al-Shomrani,2015hq-supplemented subgroups on the structure of finite groups.]]>Elkholy, A.M. and M.H. Abd El-Latif,2014Mohamed, M.E. and M.I. Elashiry,2016Mohamed, M.E. and M.M. Alshomrani,2014Li, Y. and X. Zhong,2014∗-subgroups.]]>Srinivasan, S.,1980Asaad, M.,1975Huppert, B.,1979Ramadan, M., M.E. Mohamed and A.A. Heliel,2005