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.

中文翻译：

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关于有限群的弱s-半置换或ss-准正规子群

假设G是一个有限群，而H是G的一个子群。ħ据说是弱š在-semipermutable ģ如果存在低于正常的子群Ť的ģ和š -semipermutable子组\（{H_ SSG} \）的ģ包含在ħ使得\（G = HT \）和\ （H \ cap T \ le H_ {ssG} \）；ħ被说成是一个SS的子群-quasinormal ģ如果有一个子群乙的ģ使得\（G = HB \）和H对应于B的每个Sylow子组。我们固定在每一个非环状西洛子群P的ģ一些子组d满足\（1 <| d | <| P | \）和研究的结构ģ的假设下，每个子组ħ的P与\（| H | = | D | \）在G中是弱s-半置换的或ss-准正规的。最近的一些结果是概括和统一的。