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Strong hypergroups of order four arising from extensions. (English) Zbl 1166.43002

The paper under review investigates the extension problem of finite commutative hypergroups, which is essential to understand the full structure of hypergroups. By establishing the complete parametrization of commutative hypergroup extensions of a hypergroup of order two by another hypergroup of order two, the authors characterize all strong hypergroups and splitting extensions, and determine all strong hypergroups of order four which have non-trivial subhypergroups. The corresponding results for hypergroups of order three were given by N. J. Wildberger in [J. Pure and Appl. Algebra, 174, No.1, 95-115 (2002; Zbl 1008.43005)].

MSC:

43A62 Harmonic analysis on hypergroups
20N20 Hypergroups

Citations:

Zbl 1008.43005
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