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 $Q\le P$ such that $Q$ and $R$ are isomorphic via $\mathcal{F}$, $|N_P(Q)|\le |N_P(R)|$.

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