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On weakly closed subgroups of finite groups |
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| Authors: | Zhencai Shen Yingyi Chen Shirong Li |
| Institution: | 1. Department of Mathematics of College of Science, China Agricultural University, Beijing, ?100083, China 2. College of Information and Electrical Engineering, China Agricultural University, Beijing, ?100083, China 3. Department of Mathematics, Guangxi University, Nanning, ?530004, Guangxi, China |
| Abstract: | Suppose that \(G\) is a finite group and \(H\) , \(K\) are subgroups of \(G\) . We say that \(H\) is weakly closed in \(K\) with respect to \(G\) if, for any \(g \in G\) such that \(H^{g}\le K\) , we have \(H^{g}=H\) . In particular, when \(H\) is a subgroup of prime-power order and \(K\) is a Sylow subgroup containing it, \(H\) is simply said to be a weakly closed subgroup of \(G\) or weakly closed in \(G\) . In the paper, we investigate the structure of finite groups by means of weakly closed subgroups. |
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