A generalization of Burnside’s p-nilpotency criterion

Abstract

Abstract Let p be a prime number, let G be a finite group, and let P be a Sylow p-subgroup of G. Under the assumption that N G ⁢ ( P ) ${N_{G}(P)}$ is p-nilpotent, we give an equivalent condition of the p-nilpotency of G. Our result is a generalization of the famous Burnside p-nilpotency criterion and some recent results.