Singular neutrosophic extended triplet groups and generalized groups

Abstract

Neutrosophic extended triplet group (NETG) is an interesting extension of the concept of classical group, which can be used to express general symmetry. This paper further studies the structural characterizations of NETG. First, some examples are given to show that some results in literature are false. Second, the differences between generalized groups and neutrosophic extended triplet groups are investigated in detail. Third, the notion of singular neutrosophic extended triplet group (SNETG) is introduced, and some homomorphism properties are discussed and a Lagrange-like theorem for finite SNETG is proved. Finally, the following important result is proved: a semigroup is a singular neutrosophic extended triplet group (SNETG) if and only if it is a generalized group.