Essential 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

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 ${\mathcal {F}}$-essential subgroup of $P$ if it is ${\mathcal {F}}$-centric and if $\operatorname {Aut} _{\mathcal {F}}(Q)/\operatorname {Aut} _{Q}(Q)$ has a strongly p-embedded subgroup.