Abelian subgroups based on neutrosophic sets

Aiyared Iampan1,∗, C. Sivakumar2, P. Maragatha Meenakshi3, N. Rajesh4

1Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur

Mueang, Phayao 56000, Thailand

2,3Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to

Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India

4Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India

Emails: aiyared.ia@up.ac.th1; sivaias777@gmail.com2; maragathameenakship@gmail.com3;

nrajesh topology@yahoo.co.in4

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.

Keywords: neutrosophic group; neutrosophic Abelian subgroup; neutrosophic cyclic subgroup.