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Estimation of the orders on hypergroup extensions. (English) Zbl 1201.43003

Let \(K\) be a finite commutative signed hypergroup with subhypergroup \(H\). The authors study properties of \(K\) for given \(H\) and for the given quotient hypergroup \(K/H\). In particular, the order \(|K|\) and the weight \(w(K)\) are estimated where \(w\) is the Haar measure of \(K\) with normalization \(w(\{e\})=1\) for the identity \(e\in K\). The authors give also examples which show that the estimates are sharp. The extreme cases are constructed by using direct products and joins.

MSC:

43A62 Harmonic analysis on hypergroups
20N20 Hypergroups
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