Radical subgroup for a fusion system

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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).