Document Type : Research Paper

Authors

• Sunday Adesina Adebisi ¹
• Florentin Smarandache ²

¹ Department of Mathematics, Faculty of Science, University of Lagos, Akoka, Yaba, Nigeria.

² Department of Mathematics, University of New Mexico, Gallup Campus, NM 87301, USA.

Abstract

The neutrosophic automorphisms of a neutrosophic groups  G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of  G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X₁ = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and X_n the neutrosophic group of inner neutrosophic automorphisms of X_n-1. In this paper, we show that if any neutrosophic group of the sequence G (I), X₁, X₂, … is the identity, then G (I) is nilpotent.

Keywords

• Neutrosophic automorphism
• Commutator subgroup
• Neutrosophic subgroup
• Minimal condition
• Mapping composition
• Nilpotency

Main Subjects

• Neutrosophic sets and their variants