The article defines a subgroup property, where the definition may be in terms of a particular prime number that serves as parameter
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A group that has a normal -complement is termed a p-nilpotent group.
Definition with symbols
- is normal in and there is a Sylow -subgroup of such that and is trivial.
- is normal in and for every Sylow -subgroup of , and is trivial.
- is a normal Hall subgroup of whose order is relatively prime to and whose index is a power of . In other words, is a normal -Hall subgroup of .
If contains a normal -complement , we say that is a p-nilpotent group.
A complete list of normal p-complement theorems is available at: