Finite groups admitting a fixed-point-free 2-automorphism

It is proved that if a finite group admits a fixed-point-free automorphism of order 2ⁿ, then its nilpotent length is at most n. It had been proved by Gross [1] that its nilpotent length is at most 2n–2.Translated from Matematicheskie Zametki, Vol. 23, No. 5, pp. 651–657, May, 1978.