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Journal of Applied Sciences
  Year: 2017 | Volume: 17 | Issue: 3 | Page No.: 148-152
DOI: 10.3923/jas.2017.148.152
 
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On 𝔍hq-supplemented Subgroups of a Finite Group

M. Ezzat Mohamed, Mohammed M. Al-Shomrani and M.I. Elashiry

Abstract:
Background 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.
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How to cite this article:

M. Ezzat Mohamed, Mohammed M. Al-Shomrani and M.I. Elashiry, 2017. On 𝔍hq-supplemented Subgroups of a Finite Group. Journal of Applied Sciences, 17: 148-152.

DOI: 10.3923/jas.2017.148.152

URL: https://scialert.net/abstract/?doi=jas.2017.148.152

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