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. In this note, we fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the p-nilpotency of G under the assumption that every subgroup H of P with |H| = |D| is SS-quasinormal in G. The Frobenius theorem is generalized.

中文翻译：

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有限群 p 幂零性的新表征

假设G是一个有限群并且H是一个子群G.H据说是一个小号小号- 的拟正规子群G如果有一个子组乙的G这样G = H乙和H与每个 Sylow 子群置换乙. 在本笔记中，我们固定在每个非循环 Sylow 子群中磷的G一些子群D令人满意的1 < |D| < |磷|并研究p- 的全能性G假设每个子组H的磷和|H| = |D|是小号小号- 准正常G. Frobenius 定理是广义的。