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 ℋC-embedded in G if G has a normal subgroup T such that HG = HT and NT(H) ∩ Hg ≤ H for all g ∈ G, where HG is the normal closure of H in G. In this paper, we study the p-nilpotence of a group G in which every subgroup of order d of a Sylow p-subgroup P with 1 < d < |P| is weakly ℋC-embedded in G. Many recent results in the literature related to p-nilpotence of G are generalized.

中文翻译：

---

关于弱ℋC-嵌入子群和有限群的p-幂零

让G是一个有限群并且H一个子群G. 我们说H是一个ℋ-子群G如果ñG(H) ∩ HG ≤ H对全部G ∈ G;H被弱称为ℋC-嵌入G如果G有一个正规子群吨这样HG = H吨和ñ吨(H) ∩ HG ≤ H对全部G ∈ G,在哪里HG是正常的关闭H在G. 在本文中，我们研究了p- 群的幂零性G其中每个子组的顺序d西洛的p-子群磷和1 < d < |磷|弱ℋC-嵌入G. 文献中的许多最新结果与p- 无能G是广义的。