THE NEUTROSOPHIC HOM - GROUPS AND NEUTROSOPHIC HOM - SUBGROUPS I

Abstract

Hom-groups are the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. The neutrosophic set is a powerful tool in dealing with incomplete, indeterminate and inconsistent data that exist in the real world. Neutrosophic set is characterized by the truth membership function in the set (T), indeterminacy membership function in the set (I) and falsity membership function in the set (F) where 0   T + I + F   3+. In this work, e orts are intensi ed to clearly exemplify and create distinctions between certain structural ( classical ) groups , which are neutrosophic Hom groups and those which are not. Some examples of the neutrosophic Hom groups are also carefully constructed with elementary features and characterizations such as the subgroup series as well as their lattices.

Finally , the certainty of the Lagranges theorem involving the subgroup of any nite neutrosophic Hom - group G(I)