تفاصيل الرسالة العلمية

Extensions of polygroups such as direct hyper product and wreath product of polygroups have been introduced and studied by Comer, 1982. In this thesis, we define and study several other extensions. We first present regularly normal subpolygroups and prove that they induce a quotient polygroup extensions. In addition, we prove that the kernel of every strong homomorphism is a regularly normal subpolygroup. This leads to present new versions of the isomorphism theorems with respect to such subpolygroups. The main objective of this thesis is to present a new extension of polygroups by polygroups via factor polygroups which is a generalization of both the direct hyper product and the wreath product of polygroups. Let H and L be polygroups and I be a regularly normal subpolygroup of H. We introduce the extension K of L by H via the factor polygroup H/I. This extension has H as a regularly normal subpolygroup and the cosets of H in K has the same cardinality as that of H/I. We finally, present a special case when L is a symmetric polygroup. In this case, we can obtain extensions of L by H via factor polygroups H/I with arbitrary choice of cosets of cardinalities as that of H/I