有限群可解的一个充分条件

A Sufficient Condition for Solvability of Finite Groups

证明了如下定理:设G是有限群,π_e(G)是G中元素的阶之集,如果π_e(G)∩{2}=Ф,或π_e(G)∩{3,4}=Ф,或π_e(G)∩{3,5}=Ф,则G可解.进一步,用与π_e(G)的交为空集来判定G可解,仅有上述3种情形.

The following theorem is proved： Let G be a finite group and πe （G） be the set of element orders in G. If πe （G）∩ {2} =Ф, or πe （G）∩ {3, 4} = Ф, or πe （G）∩{3, 5} = Ф, then G is solvable. Furthermore, using the intersection with πe （G） being empty set to judge G is solvable or not, only the above three cases.