P-nilpotent group

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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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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.