On Finite Groups with Transfer Maps and Weak Closure
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6859Keywords:
finite groups, weakly closed subgroup, Sylow p-subgroupAbstract
Let G be a finite group, P ∈ Sylp(G) and W ⊆ P. We say that W is weakly closed in P with respect to G if Wg ⊆ P. In this paper, we explore structural properties of finite groups using the transfer homomorphism and the notion of weak closure in Sylow subgroups. We establish that if a central subgroup H ≤ Z(G) has finite index [G : H] coprime to | H |, then G ∼=H × ker(v), where v : G → H is the transfer. Furthermore, we characterize weakly closed subgroups W ≤ P ∈ Sylp(G) as normal in both NG(P) and all Sylow p subgroups containing W. Several consequences concerning conjugacy and normality are discussed.
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Copyright (c) 2025 Abdulaziz Alotaibi, khalid Al-Tahat, Khaled Mustafa Aljamal
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