Hi. I want to talk about the derivation of the form of space-time transformations T between inertial references. As it's known, this is the Poincaré group, defined as the group that leaves invariant the (+,-,-,-) metric. This derives from two things: c is constant and space-time is homogeneous and isothropic. Now, I understand that the fact that c is constant defines the conformal group, that leaves the metric invariant up to a generic multiplicative number f(x,T) (that depends on the coordinates and, of course, on the transformation considered). But I don't understand why the homogeneity and isotropy implies f(x,T) = 1. Normally, by homogeneity I mean that if T(x) is in the group, then so does T(x) + a (a is a generic vector), and by isotropy I mean that also T(R(x)) (R is a generic rotation) is in the group. But this doesn't imply f = 1, as translations and rotations are already in the conformal group. Somebody can explain? What is the exact mathematical meaning of homogeneity and isotropy?