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Finite Groups with Weakly Subnormal and Partially Subnormal Subgroups
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2021-01-29 , DOI: 10.1134/s0037446621010183 J. Huang , B. Hu , A. N. Skiba
中文翻译:
具有弱次正规子群和部分次正规子群的有限群
更新日期:2021-01-29
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2021-01-29 , DOI: 10.1134/s0037446621010183 J. Huang , B. Hu , A. N. Skiba
We study the influence of weakly subnormal and partially subnormal subgroups on the structure of a group \( G \). In particular, we prove that a finite group \( G \) is supersoluble if and only if \( G=AB \), where \( A \) and \( B \) are supersoluble weakly subnormal subgroups in \( G \), and every Schmidt subgroup in \( G \) is partially subnormal in \( G \).
中文翻译:
具有弱次正规子群和部分次正规子群的有限群
我们研究了弱次正规子群和部分次正规子群对\(G \)群结构的影响 。特别地,我们证明了当且仅当\(G = AB \)时,有限组 \(G \)是超溶的 ,其中 \(A \)和 \(B \)是 \(G \ ),并在每一个施密特子群 \(G \) 是部分地低于正常在 \(G \) 。