含极大子群为单群的单群

The Simple Group Which Possess Some Simple Groups as the Maximal Subgroup

从极大子群的角度探讨了原群的单性,得到:(ⅰ)设群G的任一极大子群都是单群,若G中存在一个非正规极大子群满足性质(φ),那么G是单群.设群G的极大子群都非正规,且极大子群要么为单群要么为幂零群,则:(ⅱ)如果两者都存在,且其中有一个幂零极大子群为有限群,那么G为单群.(ⅲ)如果其中有一个幂零极大子群为有限生成群,有一个单极大子群为周期群,那么G为单群.(ⅳ)如果其中有一个幂零极大子群M和一个单极大子群R使得R∩MperM,那么G为单群.

In this paper, we investigate relationship between the simplicity of groups and their maximal subgroups and get the following results： （i） Let every maximal subgroup of group G be simple. If there is a nonnormal maximal subgroup of G which possesses property （φ）, then G is simple. tent： Let every maximal subgroup of group G be nonnormal and every maximal subgroup be simple or nilpotent： （ii） if both （iii） if there group which is of them are existent, are a nilpotent ma torsion, then G is s xi and one of the maximal subgroups mal subgroup which is finitely gen imple. of era G is finite, then G is simple. ted and a simple maximal sub-group which is torsion, then G is simple. （iv） if there are a nilpotent maximal subgroup M and a simple maximal group R which satisfy R ∩ M per M, then G is simple.