Characteristic p-functor that controls normal p-complements

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This article defines a property that can be evaluated for a characteristic p-functor in the context of a finite group.|View other such properties

Definition

Suppose p is a prime number and W is a characteristic p-functor. We say that W controls normal p-complements in a finite group G if the following holds: if there exists a p-Sylow subgroup P, such that N_G(W(P)) possesses a normal p-complement, G also possesses a normal p-complement.

We say that W controls normal p-complements in general if it controls normal p-complements in every finite group.

Facts