Groups and Lie algebras with almost regular automorphisms (Q1325076)

The author proves that a nilpotent group \(G\) with an almost regular automorphism \(\varphi\) of prime order \(p\) contains a nilpotent subgroup \(G_ 1\) such that \(| G : G_ 1|\) is \((p,m)\)-bounded, where \(m\) is the number of fixed points of \(\varphi\), and the class of nilpotency of \(G_ 1\) is \(p\)-bounded. An analogue is then proved for Lie rings (not necessarily locally nilpotent).