Quaternionic groups in physics

We study the left and right action of quaternionic numbers. The standard problems arising in the definitions of transpose, determinant, and trace for quaternionic matrices are overcome. We investigate the possibility of formulating 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 and right operators as fundamental step toward a clear and complete discussion of unification theories in physics.