essential subgroup

A subgroup $H$ of a group $G$ is essential if $H\cap K\ne \left\{e\right\}$ for any subgroup $K$ of $G$, $K\ne \left\{e\right\}$ (i.e., a subgroup $H$ of $G$ is called essential if it intersects non-trivially everynon-trivial subgroup of $G$).