Some Elementary Combinatorial Properties of Aktas' Soft Groups with Contributions in Soft Actions (Journal of Informatics and Mathematical Sciences, 2016)
As a generic mathematical tool, the concept of soft sets introduced in 1999 by Molodtesov, and in continuation of this research the soft groups defined and studied for their nice properties by Aktas in 2007. Because of the extensive applications of soft sets and soft groups in all branches of sciences involving mathematics we prefer to concentrate on the algebraic properties of algebraic structures. The action of groups on sets is an effective instrument in algebra. In this note we drive some basic combinatorial properties of soft groups using Aktas's definition of soft group and soft subgroups. By giving the definition of soft actions of groups and semigroups we managed to exhibit their congruence properties in this paper.
Keywords: Soft set; Soft semigroup; Soft group; Soft subgroup; Soft action; Congruence