Groups and Lie Algebras with Almost Regular Automorphisms Original Research Article

It is proved that if a locally nilpotent group G admits an almost regular automorphism of prime order p then G contains a nilpotent subgroup G1 such that G : G1≤ƒ(p, m) and the class of nilpotency of G1ƒg(p), where ƒ is a function on p and the number of fixed elements m and g depends on p only. An analog is proved for Lie rings (not necessarily locally nilpotent). These give an affirmative answer to the questions raised by Khukhro.