关于有限2—拟质元群

The Sort of the Finite 2-Quasi-Prime Element Group

文章推广了文献[3]、[14]的工作,研究元的阶至多含二个合数的有限群(称之为2—拟质元群),并给出了它们的完全分类.得到了一般结果:若G是2—拟质元群,则|π(G)|≤5,且当|π(G)|=5时,有:G为单群.用S(G)表示群G的可解根基,πe″(G)表示πe(G)中的合数集合,{πi,i=1,2,…,t}表示G的各连通素图分支,π1表示含2的连通分支.

This paper developed the result of ?.And it has reseached the finite group,be denoted 2-QPE-group,that its set of element's orders has only two composites.We have sorted the 2-QPE-groups.and we get the result:If a group G is a 2-QPE-group,then |πe(G)|≤5.When |πe(G)|=5,the group G is a simple group.