关于有限群的一个问题

ON A PROBLEM OF FINITE GROUPS

设G是有限群,在这篇短文中,我们证明了下面的定理:定理 如果Aut(G)二重可迁地作用在G的所有同阶元集合上,则G同构于下列三群之一:(Ⅰ)3阶循环群(Ⅱ)3次对称群(Ⅲ)2~α阶初等Abel群,α>1.

Let G be a finite group and let M be the set of elements of order i. In this paper, the author has proved the following result: .Theorem If the action of Aut(G) on all Mi is double transitive, then G is isomorphic to one of the groups of the following list:( I ) Cyclic group of order 3.( II ) Symmetric group of degree 3.( III ) Elementary abelian 2-group of order 2, a>1.