P-nilpotent group

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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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 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. $O_{p',p}(G)=G$.