P-nilpotent group

Definition
A finite group $$G$$ is termed a p-nilpotent group for a prime number $$p$$ if the following equivalent conditions are satisfied:


 * 1) $$G$$ has a defining ingredient::normal p-complement, i.e., a normal Hall subgroup whose order is coprime to $$p$$ and whose index is a power of $$p$$.
 * 2) The $$p$$-Sylow subgroups of $$G$$ are retracts of $$G$$.
 * 3) $$O_{p',p}(G) = G$$.