On ss-quasinormal or weakly s-permutably embedded subgroups of finite groups

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• 作者：Qingjun Kong ; Xiuyun Guo
• 关键词：ss ; quasinormal ; Weakly s ; permutably embedded ; Saturated formation
• 刊名：Monatshefte für Mathematik
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：182
• 期：3
• 页码：637-647
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：182

文摘

Suppose that G is a finite group and H is a subgroup of G. 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; H is said to be weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup \(H_{se}\) of G contained in H such that \(G=HT\) and \(H\cap T\le H_{se}\). 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 ss-quasinormal or weakly s-permutably embedded in G. Some recent results are generalized and unified.