Supernormal subhypergroup

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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)

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 groupK is said to be normal if xHx^{-1} = H for any x \in K.

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