On a special single-power cyclic hypergroup and its automorphisms

Abstract

After introducing the definition of hypergroups by Marty, the study of hyperstructures and its applications has been of great importance. In this paper, we find a link between hyperstructures and the infinite non-abelian group, braid group [Formula: see text]. This is the first connection to be done between these two different domains. First, we define a new hyperoperation ⋆ associated to [Formula: see text] and study its properties. Next, we prove that [Formula: see text] is a single-power cyclic hypergroup with infinite period. Then, we define an onto homomorphism from [Formula: see text] to another hypergroup. Finally, we determine the set of all automorphisms of [Formula: see text] and prove that it is a group under the operation of functions composition.