Soft Groups and Characteristic Soft Subgroups

Abstract

Group theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of the soft group, the kernel of soft homomorphism and soft automorphisms with their basic properties. Furthermore, the concept of soft point groups is introduced and the properties of these soft groups are studied. We state the concept of characteristic soft subgroups of a given soft group. Also, some theorems related to this concept are investigated. We study the characteristic soft subgroups of a given soft point group. The characteristic soft subgroups play a significant part in the study of the soft group theory and are useful for understanding the structure of a soft group and its soft automorphisms. As an application of characteristic soft subgroups, they allow us to identify and study important soft subgroups that are preserved under soft automorphisms. Also, practical applications for our theory can be conducted in future work such as the relation with other disciplines in sciences.