On weakly s-semipermutable or ss-quasinormal subgroups of finite groups |
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Authors: | Kong Qingjun Guo Xiuyun |
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Institution: | 1.Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China ;2.Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China ; |
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Abstract: | Suppose that G is a finite group and H is a subgroup of G. H is said to be weakly s-semipermutable in G if there are a subnormal subgroup T of G and an s-semipermutable subgroup \(H_{ssG}\) of G contained in H such that \(G=HT\) and \(H\cap T\le H_{ssG}\); H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that \(G=HB\) and H permutes with every Sylow subgroup of B. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying \(1<|D|<|P|\) and study the structure of G under the assumption that every subgroup H of P with \(|H|=|D|\) is either weakly s-semipermutable or ss-quasinormal in G. Some recent results are generalized and unified. |
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