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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Centers of hypergroups


Author: Kenneth A. Ross
Journal: Trans. Amer. Math. Soc. 243 (1978), 251-269
MSC: Primary 43A10; Secondary 22A99
MathSciNet review: 0493161
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0493161-2
PII: S 0002-9947(1978)0493161-2
Keywords: Hypergroup, center of hypergroup, character hypergroup, Z-group, automorphism group, orthogonality relations, measure algebras
Article copyright: © Copyright 1978 American Mathematical Society