Abelian subgroups based on neutrosophic sets

Abstract

The notion of a neutrosophic Abelian subgroup of a group is introduced. The characterizations of a neutrosophic Abelian subgroup are investigated. We show that the homomorphic preimage of a neutrosophic Abelian subgroup of a group is a neutrosophic Abelian subgroup, and the onto homomorphic image of a neutrosophic Abelian subgroup of a group is a neutrosophic Abelian subgroup.