On hypercyclic fully zero-simple semihypergroups

Let I be the class of fully zero-simple semihypergroups generated by a hyperproduct. In this paper we study some properties of residual semihypergroup (H_+; star) of a semihypergroup (H; \u25e6)in I. Moreover, we find sufficient conditions for (H; \u25e6) and (H_+; star) to be cyclic

On Further Properties of Fully Zero-Simple Semihypergroups

Let $mfF_0$ the class of fully zero-simple semihypergroups. In this paper we study the main properties of residual semihypergroup $(H_+, star)$ of a semihypergroup $(H, circ)$ in $mfF_0$. We prove that the quotient semigroup $H_+/eta^*_{H_+}$ is a completely simple and periodic semigroup. Moreover, we find the necessary and sufficient conditions for $(H_+, star)$ to be a torsion group and, in particular, an Abelian $2$-group

1-hypergroups of small sizes

In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation \u3b2. Many of these hypergroups can be obtained using the aforesaid hypergroup construction