In this work we explore the connection between group theory and transformations among frames of reference. Starting from the very definition of representations of the abstract Galileo and Lorentz groups over the space-time, we are naturally led to the Galileo and Lorentz transformations in classical and relativistic regime. In addition to providing an introductory material for advanced topics, such as group theory and its representations, this paper also brings an alternative formulation to the special relativity theory.
principle of relativity; group theory; special relativity
