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Zbl 0810.20057
Corsini, P.; Freni, D.
On the heart of hypergroups. (English)
[J] Math. Montisnigri 2, 21-27 (1993). ISSN 0354-2238

Let $H$ be a hypergroup and consider on $H$ the relations $(\beta\sb n)\sb{n \in \bbfN\sp*}$ defined by: $x \beta\sb 1 y$ if and only if $x = y$ and if $n \geq 2$ then $x \beta\sb n y$ if and only if there exists $(x\sb 1, \dots, x\sb n) \in H\sp n$ such that $x$ and $y$ are in $x\sb 1 x\sb 2 \dots x\sb n$. The relation $\beta = \bigcup\sb{n \in \bbfN\sp*} \beta\sb n$ is an equivalence relation on $H$, it is strongly regular and $H / \beta$ is a group [see {\it P. Corsini}, Prolegomena of Hypergroup Theory. (1993; Zbl 0785.20032)]. If 1 is the identity of the group $H /\beta$ and $p : H \to H/\beta$ is the canonical projection then $\omega\sb H = p\sp{-1} (1)$ is called the heart of $H$.\par The purpose of this paper is to characterize the hypergroups $H$ for which the heart is a hyperproduct, i.e. there exist $n \in \bbfN\sp*$ and $(x\sb 1, \dots, x\sb n) \in H\sp n$ such that $\omega\sb H = x\sb 1 \dots x\sb n$.
[M.Guţan (Aubière)]

MSC 2000:: *20N20 Hypergroups (group theory)

Keywords: semiregular hypergroups; equivalence relation; strongly regular; hypergroups; heart; hyperproduct

Citations: Zbl 0785.20032

Cited in: Zbl 0842.20059

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