Normal subhypergroup

From Groupprops
Jump to: navigation, search
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)


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.


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

Weaker properties