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 $R\le P$, and any morphism $\phi$ in $\mathcal{F}$ from $R$ to $P$, we have:

$\phi (R\cap Q)\le Q$

Relation with other properties

Weaker properties

• Weakly closed subgroup for a fusion system