A generalized fixed point free automorphism of prime power order

Ercan, Gülin
Güloǧlu, Ismail Ş.
Let G be a finite group and alpha be an automorphism of G of order p(n) for an odd prime p. Suppose that alpha acts fixed point freely on every alpha-invariant p'-section of G, and acts trivially or exceptionally on every elementary abelian alpha-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.