On the folding of groups

Abstract

The aim of this work is to introduce a new type of folding called a group folding of a group into a special proper subgroup which induced a graph folding into the identity graph of the group.Also we prove that the composition of such foldings is again a group folding.we find some types of groups which have a normal group folding.Finally we discuss the relation between matrices and group folding.Theorems governing these types of foldings are achieved.