剩余有限minimax 可解群的几乎正则自同构

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α^p = 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.关键词剩余有限minimax 可解群几乎正则自同构

On almost regular automorphisms of residually finite minimax soluble groups

Let G be a residually finite minimax soluble group and α be an almost regular automorphism of G. Then G=[G;α] is a finite group. If α^p = 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.