可解NPM-群

Solvable NPM-grou

讨论了阶被|G|的最小素因子p整除的所有非正规循环子群的正规化子皆极大的可解群(文中称满足条件的群为NPM-群)。得到了下面结果:(1)G为可解NPM-群且G的Sylow p-子群P为G的极大子群时给出了G的结构;(2)若G为可解NPM-群且P不是G的极大子群,则G或者为p-闭群,或者为p-幂零群。

In this paper, we concenter a class of group such that all the non-normal cyclic subgroup whose order are divided by the minimal divider p of ｜G｜ have maximal normalizer（we call such a group an NPM-group）. We give some properties of solvable NPMgroup.（1） If G is an NPM-group and the Sylow p-subgroup P of G is maximal in G, then we give the structure of G;（2） If G is an NPMgroup and P is not maximal in G, then G is either p-closed or p-nilpotent.