Subgroup fully normalized by a category

This article defines a property that can be evaluated for a group of prime power order, equipped with a fusion system
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Definition

Suppose $P$ is a group of prime power order and ${\mathcal {F}}$ is a category on $P$. A subgroup $R$ of $P$ is termed fully normalized by ${\mathcal {F}}$ if, for any $Q\leq P$ such that $Q$ and $R$ are isomorphic via ${\mathcal {F}}$, $|N_{P}(Q)|\leq |N_{P}(R)|$.

The definition is typically used when ${\mathcal {F}}$ is a fusion system on $P$.