Soft uni-group and its applications to group theory

Abstract

In this paper, we define soft union group, serving as a bridge among soft set theory, set theory and group theory and showing how a soft set effects on a group structure in the mean of union and inclusion of sets. We then derive its basic properties and relation with the notion of soft intersection group and obtain some analog of classical group theoretic concepts for soft union group. Moreover, we give some applications of soft union groups to group theory.