Normal subhypergroup

ANALOGY: This is an analogue in hypergroups of the subgroup property:
View other analogues of normality | View other analogues in hypergroups of subgroup properties

Definition

Symbol-free definition

A subhypergroup of a hypergroup is said to be normal if it commutes with every point measure.

Definition with symbols

A subhypergroup $H$ of a hypergroup $K$ is said to be normal if $H*x=x*H$ for every point $x\in K$.

Analogy

The notion of normality for subhypergroup is analogous to the subgroup property of normality, when defined/viewed as follows:

A subgroup $H$ of a group $K$ is termed normal if $Hx=xH$ for all elements $x\in K$.

Relation with other properties

Stronger properties

• Supernormal subhypergroup

Weaker properties

• Subhypergroup