Frobenius conjecture

Statement
The Frobenius conjecture has the following equivalent formulations:


 * A Frobenius kernel (proper nontrivial centrally closed normal subgroup) in a finite group must be nilpotent
 * If a finite group possesses a fixed-point-free automorphism whose order is prime, then the finite group must be nilpotent

The Frobenius conjecture has been proved by Thompson in his paper Finite groups with fixed-point-free automorphisms of prime order.