Focal series of a subgroup

This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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Definition

Suppose $H$ is a subgroup of a group $G$. The focal series of $H$ in $G$ is a series $H=H_{0}\geq H_{1}\geq H_{2}\geq \dots$ where we define:

$H_{n+1}=\operatorname {Foc} _{G}(H)$.

In other words, each member of the series is the focal subgroup of its predecessor. The focal subgroup is defined as:

$\operatorname {Foc} _{G}(K)=\langle xy^{-1}\mid x,y\in K,\exists g\in G,gxg^{-1}=y\rangle$.

A subgroup whose focal series terminates at the trivial subgroup is termed a hyperfocal subgroup.