On Normal and Soft Normal Groups under Multisets and Soft Multiset Context

Idris Muhammadu Adamu, Y. Tella, A. J. Alkali

Abstract


In this paper, the concepts of normal submultigroups and soft normal multigroups with some of their related algebraic structures were developed. We established that intersection, union of any two normal submultigroups is also normal submultigroup of a given multigroup. The inverse of any normal submultigroup of a multigroup is a normal submultigroup and for any normal submultigroup, the root (support) set is a normal subgroup of the underlying group.  We then showed that under the isomorphism function between any two groups, the image of a normal submultigroup under the isomorphism is a normal submultigroup and the inverse image of a normal submultigroup under the isomorphism is a normal submultigroup. Finally, we defined operations on soft normal multigroups such as intersection, union, AND, OR operations and discovered that such operations are closed under soft normal multigroups.


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