On almost regular automorphisms of residually finite minimax soluble groups

Abstract

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