Core of a subgroup (awaiting review)

If $G$ is a group and $H$ is a subgroup of $G$, then the core of $H$ in $G$ is the subgroup \[ \textrm{Core}(H) = \bigcap_{g\in G} gHg^{-1}.\] Equivalently, $\textrm{Core}(H)$ is the largest normal subgroup of $G$ contained in $H$.