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We consider the class of 0-semigroups (H, ?) that are obtained by adding a zero element to a group (G, ·) so that for all x, y ∈ G it holds x? y , 0 ⇒ x? y = xy. These semigroups are called 0-extensions of (G, ·). We introduce a merging operation that constructs a 0-semihypergroup from a 0-extension of (G, ·) by a suitable superposition of the product tables. We characterize a class of 0-simple semihypergroups that are merging of a 0-extension of an elementary Abelian 2-group. Moreover, we prove that in the finite case all such 0-semihypergroups can be obtained from a special construction where (H, ?) is nilpotent.

Semihypergroups obtained by merging of 0-semigroups with groups