A subgroup H of a finite group G is said to be weakly \(\mathcal {H}C\)-embedded in G if there exists a normal subgroup T of G such that \(H^G = HT\) and \(H^g \cap N_T(H) \le H\) for all \(g \in G\), where \(H^G\) is the normal closure of H in G. In this paper, we investigate the structure of the finite group G under the assumption that P a Sylow p-subgroup of G, where p is a prime dividing the order of G, and we fix a subgroup of P of order d with \(1< d < \left| P\right| \) such that every subgroup H of P of order \(p^nd ~(n = 0, 1)\) is weakly \(\mathcal {H}C\)-embedded in G.

中文翻译：

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$$ \ mathcal {H} C $$ H C-嵌入式子组的有限组

一个分组ħ有限群G ^据说是弱\（\ mathcal {H}℃\）在-嵌入式ģ如果存在一个正常子群Ť的ģ使得\（H ^ G = HT \）和\（ H ^克\帽N_T（H）\文件ħ\）对所有\（克\ G中\） ，其中\（H ^ g \）是正常闭合ħ在ģ。在本文中，我们研究了有限群的结构ģ在假设P一西洛p的-subgroup ģ，其中p是素分割的顺序ģ，我们固定的子组P顺序的d与\（1 <d <\左| P \右| \） ，使得每个子组ħ的P的顺序\（P ^ ND〜 （n = 0，1）\）弱\（\ mathcal {H} C \）-嵌入在G中。