On $$\mathfrak {F}_{hq}$$-supplemented subgroups of a finite group |
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Authors: | M Ezzat Mohamed Mohammed M Al-Shomrani M I Elashiry |
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Affiliation: | 1.Faculty of Arts and Science,Northern Border University,Rafha,Saudi Arabia;2.Mathematics Department, Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia;3.Department of Mathematics, Faculty of Science,Fayoum University,Faiyum,Egypt |
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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. |
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