One more derivation of the Lorentz transformation

After a criticism of the emphasis put on the invariance of the speed of light in standard derivations of the Lorentz transformation, another approach to special relativity is proposed. It consists of an elementary version of general group-theoretical arguments on the structure of space–time, and makes use only of simple mathematical techniques. The principle of relativity is first stated in general terms, leading to the idea of equivalent frames of reference connected through ’’inertial’’ transformations obeying a group law. The theory of relativity then is constructed by constraining the transformations through four successive hypotheses: homogeneity of space–time, isotropy of space–time, group structure, causality condition. Only the Lorentz transformations and their degenerate Galilean limit obey these constraints. The role and significance of each one of the hypotheses is stressed by exhibiting and discussing counterexamples, that is, transformations obeying all but one of these hypotheses.