关于s-拟正规准素子群和p-超可解群系的三个结果

Three Results on s-Quasinormal Primary Subgroups and p-Supersolvable Formation

有限群G的子群H称为G的s-拟正规子群,如果H与G的所有Sylow子群可置换。令P是G的Sylow p-子群,对于P的不包含P∩O^(p)(G)的这些极大子群而言,利用其s-拟正规性质,分别描述了p-幂零群或者p-超可解群的结构。这些结果推广了已有的定理,也为选取Sylow p-子群的极大子群提供了一种有效的方式。

A subgroup H of G is said to be s-quasinormal in finite group G if H permutes with all Sylow subgroups of G.Let P be a Sylow p-subgroups of G.For these maximal subgroups of P that do not contain P∩O^(p)(G),some new characterizations on p-nilpotent groups or p-supersolvable groups were obtained by utilizing their s-quasinormal properties,respectively.These results generalized existing theorems and provided an effective way to select maximal subgroups of Sylow p-subgroups.