Ichihara, Ryo; Kawakami, Satoshi Estimation of the orders on hypergroup extensions. (English) Zbl 1201.43003 Sci. Math. Jpn. 72, No. 1, 29-39 (2010). 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. Reviewer: Michael Voit (Dortmund) Cited in 2 Documents MSC: 43A62 Harmonic analysis on hypergroups 20N20 Hypergroups Keywords:finite hypergroups; exact sequences; order of hypergroups; weight of hypergroups; hypergroup extensions PDFBibTeX XMLCite \textit{R. Ichihara} and \textit{S. Kawakami}, Sci. Math. Jpn. 72, No. 1, 29--39 (2010; Zbl 1201.43003) Full Text: Link