On neutrosophic extended triplet group action

This thesis discusses neutrosophic extended triplet (NET) direct product, semi-direct product and NET group actions. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce NET internal and external direct and semi-direct products for NET group by utilizing the notion of NET set theory of Smarandache. We also give examples and discuss their difference with the classical one. The action of NETG N on a NET set X is given and the difference between right and left NETG actions are briefly discussed. Then, we define fixed points, orbits and stabilizers on NET set with examples. We show that all units modulo n isn't NETG. Furthermore, we give and proof the fundamental theorem about NETG actions. Finally, we give conclusions. Key Words: NET set, Direct Products of NETG, NET Internal Direct Product, NET External Direct Product, NET Semi-Direct Product, NETG Action, Fundamental Theorem About NETG Actions, Burnside's Lemma.