Gruppi che ammettono un automorfismo 4-spezzante

LetG be a group admitting a 4-splitting automorphism (i.e. an automorphism σ such that(gg^sigma g^{sigma ^2 } g^{sigma ^3 } = 1) for everyg∈G). In this paper we prove that ifG≠1 is solvable with derived lengthd thenG′ is nilpotent of class not greater than (4 ^d?1?1)/3.