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.

Some Results on Various Cancellative CA-Groupoids and Variant CA-Groupoids

“…As a direction of future research, we will discuss the structural characteristics of CA-rings, CA-semirings and related algebraic systems (see [36][37][38][39]).…”

On Neutrosophic Extended Triplet LA-hypergroups and Strong Pure LA-semihypergroups

“…Wu prove that the construction theorem of NETG in Reference [20]; The concept of generalized neutrosophic extended group were proposed by Y.C. Ma and the relationships of NETGs and generalized groups were studied in References [21,22]. In particular, the notions of NET-semihypergroup and NET-hypergroup were introduced by X.H.…”

Neutrosophic Triplets in Neutrosophic Rings

“…Related theories of neutrosophic triplet, duplet, and duplet set were developed by Smarandache [18]. Neutrosophic duplets and triplets have fascinated several researchers who have developed concepts such as neutrosophic triplet normed space, fields, rings and their applications; triplets cosets; quotient groups and their application to mathematical modeling; triplet groups; singleton neutrosophic triplet group and generalization; and so on [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Computational and combinatorial aspects of algebraic structures are analyzed in [37].…”