Fusion system-relatively strongly closed subgroup

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Definition

Suppose $P$ is a group of prime power order and $H$ is a subgroup of $P$. We say that $H$ is a fusion system-relatively strongly closed subgroup if, for any fusion system $\mathcal{F}$ on $P$, $H$ is a strongly closed subgroup for the fusion system $\mathcal{F}$.

Relation with other properties

Stronger properties

• Variety-containing subgroup of group of prime power order

Weaker properties

• Fusion system-relatively weakly closed subgroup
• Sylow-relatively strongly closed subgroup
• Sylow-relatively weakly closed subgroup