On order of elements in hypergroups and p-Sylow subhypergroups

ABSTRACT

In this paper we define a left order, right order and order of an element in a hypergroup, which has a left scalar identity, right scalar identity and scalar identity, respectively. Using left and right orders, we define and investigate some classes of subhypergroups, especially p-Sylow subhypergroups of a hypergroup. Moreover, some examples have been proposed to show that the Sylow theorems do not hold for polygroups.

KEYWORDS:

• Homomorphism
• hypergroup
• strongly regular relations
• Sylow theorem

MATHEMATICS SUBJECT CLASSIFICATION:

• 20N20