Strongly closed 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
View other such properties

Definition

Let $P$ be a group of prime power order and ${\mathcal {F}}$ be a fusion system for $P$. A subgroup $Q$ of $P$ is termed strongly closed with respect to ${\mathcal {F}}$, if given any subgroup $R\leq P$, and any morphism $\varphi$ in ${\mathcal {F}}$ from $R$ to $P$, we have:

$\varphi (R\cap Q)\leq Q$

Relation with other properties

Weaker properties

• Weakly closed subgroup for a fusion system