In algebraic topology, the nilpotence theorem gives a condition for an element of the coefficient ring of a ring spectrum to be nilpotent, in terms of complex cobordism. It was conjectured by Ravenel (1984) and proved by Devinatz, Hopkins & Smith (1988).
Nishida's theorem
Nishida (1973) showed that elements of positive degree of the homotopy groups of spheres are nilpotent. This is a special case of the nilpotence theorem.
References
Nilpotence theorem Wikipedia(Text) CC BY-SA