Centers of hypergroups

Ross, Kenneth A.

doi:10.1090/S0002-9947-1978-0493161-2

Centers of hypergroups
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by Kenneth A. Ross

Trans. Amer. Math. Soc. 243 (1978), 251-269

DOI: https://doi.org/10.1090/S0002-9947-1978-0493161-2

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Abstract:

This paper initiates a study of Z-hypergroups, that is, commutative topological hypergroups K such that $K/Z$ is compact where Z denotes the maximum subgroup (equivalently, the center) of K. The character hypergroup ${K^\wedge }$ is studied and its connection with the locally compact abelian group ${Z^\wedge }$ is given. Each Z-group is shown to correspond in a natural way to a Z-hypergroup. It is observed that the dual of a Z-group is itself a hypergroup. The basic orthogonality relations on Z-groups due to S. Grosser and M. Moskowitz are shown to hold for most Z-hypergroups. Some results on measure algebras of compact hypergroups due to C. F. Dunkl are extended to a class of noncompact hypergroups.

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