Supernormal subhypergroup

ANALOGY: This is an analogue in hypergroup of a property encountered in group. Specifically, it is a subhypergroup property analogous to the subgroup property: normal subgroup
View other analogues of normal subgroup | View other analogues in hypergroups of subgroup properties (OR, View as a tabulated list)

History

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 $xH{x}^{-1}=H$ for any $x\in K$.

Relation with other properties

Weaker properties

• Normal subhypergroup

References

• Convergence of convolutions products of probability measures on hypergroups by W. R. Bloom and H. Heyer, Rend. Mat. Appl. 7, Serial 2, 547-563, 1982
• Connectivity and supernormality results for hypergroups by Richard C. Vrem, Math. Z. 1987