剩余有限minimax可解群的几乎正则自同构

On almost regular automorphisms of residually finite minimax soluble groups

设G是一个剩余有限的minimax可解群,α是G的几乎正则自同构,则G/[G,α]是有限群,并且(1)当αp=1时,G有一个指数有限的幂零群其幂零类不超过h(p),其中h(p)是只与素数p有关的函数.(2)当α2=1时,G有一个指数有限的Abel特征子群且[G,α]′是有限群.

Let G be a residually finite minimax soluble group and a be an almost regular automorphism of G. Then G/[G, α] is a finite group. If αp=1, then G contains a nilpotent subgroup of finite index and of nilpotent class at most h（p）, where h（p） is a function depending only on p. If α2 = 1, then G contains an abelian characteristic subgroup of finite index and [G, α]＇ is a finite group.