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Finite Groups with Weakly $$\mathcal {H}C$$ H C -Embedded Subgroups
Bulletin of the Iranian Mathematical Society ( IF 0.7 ) Pub Date : 2019-12-20 , DOI: 10.1007/s41980-019-00338-9 Qinghong Guo , Xuanli He , Jianquan Liang
Bulletin of the Iranian Mathematical Society ( IF 0.7 ) Pub Date : 2019-12-20 , DOI: 10.1007/s41980-019-00338-9 Qinghong Guo , Xuanli He , Jianquan Liang
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:
$$ \ mathcal {H} C $$ 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。
更新日期:2019-12-20
中文翻译:
$$ \ mathcal {H} C $$ 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。