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Here and in some more references it is required that the result of hyperoperation is nonempty, that is the values are in the power set without the emptyset $\mathcal{P}(X)\backslash\{\emptyset\}$. I do not know what other contributors to the page think about it.
It does not allow me to leave !include algebra - contents so I temporarily erased it. It says that it does not exist.
Added the link to the related notion of multivalued group
Maybe hypergroup should be created as this entry somehow conflates the two.
Well, there is some mess there. The page redirects also hypergroup and canonical hypergroup and canonical hypergroup also recirects hypergroup with the abstract on the latter and the definition has word canonical (what is the difference ? in equality versus subset ?). The latter page also has no references. I will do some partial remedy to it, in particular move part of the page hypermagma into canonical hypergroup and change the later to hypergoup.
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