Generalized neutrosophic extended triplet group

Abstract

Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed. In particular, the following conclusions are strictly proved: (1) an algebraic system is a generalized neutrosophic extended triplet group if and only if it is a quasi-completely regular semigroup; (2) an algebraic system is a weak commutative generalized neutrosophic extended triplet group if and only if it is a quasi-Clifford semigroup; (3) for each n ∈ Z+, n ≥ 2, (Zn,⊗) is a commutative generalized neutrosophic extended triplet group; (4) for each n ∈ Z+, n ≥ 2, (Zn,⊗) is a commutative neutrosophic extended triplet group if and only if n = p1p2 · · ·pm, i.e., the factorization of n has only single factor.