International J.Math. Combin. Vol.3(2012), 1-9 Neutrosophic Groups and Subgroups

Abstract: This paper is devoted to the study of neutrosophic groups and neutrosophic subgroups. Some properties of neutrosophic groups and neutrosophic subgroups are pre-sented. It is shown that the product of a neutrosophic subgroup and a pseudo neutrosophic subgroup of a commutative neutrosophic group is a neutrosophic subgroup and their union is also a neutrosophic subgroup even if neither is contained in the other. It is also shown that all neutrosophic groups generated by the neutrosophic element I and any group isomorphic to Klein 4-group are Lagrange neutrosophic groups. The partitioning of neutrosophic groups is also presented. Key Words: Neutrosophy, neutrosophic, neutrosophic logic, fuzzy logic, neutrosophic group, neutrosophic subgroup, pseudo neutrosophic subgroup, Lagrange neutrosophic group, Lagrange neutrosophic subgroup, pseudo Lagrange neutrosophic subgroup, weak Lagrange neutrosophic group, free Lagrange neutrosophic group, weak pseudo Lagrange neutro-sophic group, free pseudo Lagrange neutrosophic group, smooth left coset, rough left coset, smooth index. AMS(2010): 03B60, 20A05, 97H4