Radical subgroup for a fusion system

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 fusion system on $P$. A subgroup $Q$ of $P$ is termed a ${\mathcal {F}}$-radical subgroup if $O_{p}(\operatorname {Aut} _{\mathcal {F}}(Q))=\operatorname {Aut} _{Q}(Q)$. Here, $\operatorname {Aut} _{\mathcal {F}}(Q)$ denotes the automorphisms of $Q$ in the category ${\mathcal {F}}$, $O_{p}$ denotes the p-core, and $\operatorname {Aut} _{Q}(Q)$ denotes the inner automorphism group of $Q$, viewed as a subgroup of $\operatorname {Aut} _{\mathcal {F}}(Q)$.