Derivation of the lorentz transformation and their group properties

In this paper, the Lorentz transformation is derived from the two postulates: the equivalence of all inertial reference frames and the invariance of the speed of light. However, the most general transformation of space and time coordinates can be derived using only the equivalence of all inertial reference frames and the symmetries of space and time. The general transformation depends on one free parameter with the dimensionality of speed, which can be then identified with the speed of light c. This derivation uses the group property of the Lorentz transformations, which means that a combination of two Lorentz transformations also belongs to the class Lorentz transformations. This paper is organized as follows. Section (II) derivation of the Lorentz transformation. In Section (III) the study of the group property of special Lorentz transformation.