Quaternionic groups in physics

We study the left and right action of quaternionic numbers. The standard pr oblems arising in the definitions of transpose, determinant, and trace for quaternionic matrices are overcome. We investigate the possibility of formu lating a new approach to quaternionic group theory. Our aim is to highlight the possibility of looking at new quaternionic groups by the use of left a nd right operators as fundamental step toward a clear and complete discussi on of unification theories in physics.