EXTENSIONS OF POLYGROUPS BY POLYGROUPS VIA QUOTIENT POLYGROUPS

Abstract

Extensions of polygroups such as direct hyper product and wreath product of polygroups have been introduced and studied earlier by Comer. In this paper, we define and study some other extensions. We first define regularly normal subpolygroups and prove that they induce quotient polygroup extensions. In addition, we prove that the kernel of every strong homomorphism is a regularly normal subpolygroup. This leads to new versions of the isomorphism theorems with respect to such subpolygroups. The main objective of the paper is to present a new extension K of a polygroup L by a polygroup H via the quotient polygroup H/I where I is regularly normal in H. This extension is a generalization of both the direct hyper product and the wreath product of polygroups.