Let G be a finite group and H a subgroup of G. We say that H is an ℌ-subgroup of G if NG (H) ∩ Hg ≤ H for all g ∈G; H is called weakly ℌ-embedded in G if G has a normal subgroup K such that HG = HK and H ∩ K is an ℌ-subgroup of G, where HG is the normal clousre of H in G, i. e., HG = 〈Hg|g ∈ G〉. In this paper, we study the p-nilpotence of a group G under the assumption that every subgroup of order d of a Sylow p-subgroup P of G with 1 < d < |P| is weakly ℌ-embedded in G. Many known results related to p-nilpotence of a group G are generalized.
Asaad, M., Heliel, A. A. and Al-Shomranim, A. A., On weakly ℌ-subgroups of finite groups, Comm. Algebra, 40 (2012), 3540–3550.
Asaad, M., Heliel, A. A. and Al-Shomranim, A. A., On weakly ℌ-subgroups of finite groups, Comm. Algebra, 40 (2012), 3540–3550.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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