有限群的πFΦ-超中心和πFΦ-可补子群On πFΦ-hypercentre and πFΦ-supplemented Subgroups of Finite Group
张丽
摘要(Abstract)：
群G的正规子群N称为πFΦ-超中心的(πFΦ-hypercentral),如果N=1或者N≠1且N的每个阶数可被π中某些素数整除的非-Frattini G-主因子是F-中心的.群G的所有πFΦ-超中心子群的积称为G的πFΦ-超中心,并记为ZπFΦ(G).应用πFΦ-超中心定义了πFΦ-可补(πFΦ-supplemented)子群:群G的子群H称为πFΦ-可补的,如果存在G的子群T,使得G=HT且(H∩T)HG/HG≤ZπFΦ(G/HG),其中HG是G的包含在H中的最大的正规子群.研究了πFΦ-超中心的一些性质,并利用πFΦ-可补的概念给出了p-幂零和超可解的几个判断准则.
关键词(KeyWords)： Sylow子群;πFΦ-超中心;πFΦ-可补;p-幂零群
基金项目(Foundation): 国家自然科学基金资助项目,编号11371335
作者(Author): 张丽
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