By W. B. Vasantha Kandasamy

This ebook for the 1st time introduces neutrosophic teams, neutrosophic semigroups, neutrosophic loops and neutrosophic groupoids and their neutrosophic N-structures. The certain characteristic of this e-book is that it attempts to investigate while the overall neutrosophic algebraic constructions like loops, semigroups and groupoids fulfill the various classical theorems for finite teams viz. Lagrange, Sylow, and Cauchy. this is often as a rule performed to understand extra approximately those neutrosophic algebraic constructions and their neutrosophic N-algebraic buildings.

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**Additional resources for Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures**

**Example text**

A is called as the N-group-loop-semigroup-groupoid (N-glsg) if the following conditions, hold good. i. ii. e. Ai ⊆ / Aj ⊆/ or Aj ⊆/ Ai if (i ≠ j). (Ai, *i ) is a group or a loop or a groupoid or a semigroup (or used not in the mutually exclusive sense) 1≤ i ≤ N. A is a N –glsg only if the collection {A1, …, AN} contains groups, loops, semigroups and groupoids. 23: Let A = {A1 ∪ … ∪ AN, *1, …, *N} where Ai are groups, loops, semigroups and groupoids. We call a non empty subset P = {P1 ∪ P2 ∪ … ∪ PN, *1, …, *N} of A, where Pi = P ∩ Ai is a group or loop or semigroup or groupoid according as Ai is a group or loop or semigroup or groupoid.

The neutrosophic bigroups also enjoy special properties and do not satisfy most of the classical results. So substructures like neutrosophic subbigroups, Lagrange neutrosophic subbigroups, p-Sylow neutrosophic subbigroups are defined, leading to the definition of Lagrange neutrosophic 52 bigroups, Sylow neutrosophic bigroups and super Sylow neutrosophic bigroups. For more about bigroups refer [48]. 1: Let BN (G) = {B(G1) ∪ B(G2), *1, *2} be a non empty subset with two binary operation on BN (G) satisfying the following conditions: i.

A neutrosophic group is said to be pseudo simple neutrosophic group if N(G) has no nontrivial pseudo normal subgroups. We do not know whether there exists any relation between pseudo simple neutrosophic groups and simple neutrosophic groups. Now we proceed on to define the notion of right (left) coset for both the types of subgroups. 16: Let L (G) be a neutrosophic group. H be a neutrosophic subgroup of N(G) for n ∈ N(G), then H n = {hn / h ∈ H} is called a right coset of H in G. Similarly we can define left coset of the neutrosophic subgroup H in G.