Divisible Groups Derived from Divisible Hypergroups
نویسندگان
چکیده
The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the trivial divisible group. Moreover, the concept of (self) fundamental divisible group is defined and it is shown that any divisible group is a self fundamental divisible group. Finally, we study complete parts in divisible hypergroups.
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