Supernormal subhypergroup
From Groupprops
Template:Subhypergroup property
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)
Contents
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 of a hypergroup is said to be supernormal if for every element .
Analogy
The subhypergroup property of being supernormal is analogous to the subgroup property of being normal, as per the following definition: a subgroup of a group is said to be normal if for any .
Relation with other properties
Weaker properties
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