Supernormal subhypergroup

Origin
The term supernormal subhypergroup was introduced by Bloom and Heyer in their paper Cpnvergence of convolution products of probability measures on hypergroups.

Definition
A subhypergroup $$H$$ of a hypergroup $$K$$ is said to be supernormal if $$x * H * \overline{x} = H$$ for every element $$x \in K$$.

Analogy
The subhypergroup property of being supernormal is analogous to the subgroup property of being normal, as per the following definition: a subgroup $$H$$ of a group$$K$$ is said to be normal if $$xHx^{-1} = H$$ for any $$x \in K$$.

Weaker properties

 * Normal subhypergroup