中文摘要：

设G是剩余有限minimax可解群，α是G的自同构且φG→G（g→[g，α]）是满射，则有以下结果：（1）当α^p=1时，G是幂零类不超过h（p）的幂零群的有限扩张，其中h（p）是只与P有关的函数；（2）当α^4=1时，G存在一个指数有限的特征子群日，使得H″≤Z（H）和CH（α^2）是Abel群．并且Ca（α^2）和G／[G，α^2]都是Abel群的有限扩张．

英文摘要：

Let G be a residually finite minimax soluble group and α an automorphism of G. If the map φG→G defined by gφ = [g, a] is surjective, then the following hold： （1） When α^p = 1, G is （nilpotent of class at most h（p））-by-finite, where h（p） is a function depending only on p; （2） When α^4 = 1, G contains a characteristic subgroup H of finite index such that the second derived subgroup H＂ is included in the centre of H and CH（α2） is abelian. Both CG（α2） and G/[G, α^2] are abelian-by-finite.