中文摘要：

设G是有限秩的剩余有限可解群或是有限秩的剩余有限可解群的有限扩张,α是G的素数p阶几乎正则自同构,则G有一个指数有限的幂零群且其幂零类不超过h（p）,其中h（p）是只与p有关的函数.特别地,如果α是G的2阶几乎正则自同构,那么G有一个指数有限的Abel特征子群.

英文摘要：

Let G be either a residually finite soluble group of finite rank or a finite extension of a residually finite soluble group of finite rank. If G has an almost regular automorphism of prime order p, then G contains a subgroup of finite index and of nilpotent class at most h（p）, where h（p） is a function depending only on p. In particular, if G has an almost regular automorphism of order 2, then G contains an abelian characteristic subgroup of finite index.