The Galilean transformations are simple. x'=x-vt y'=y z'=z t'=t. Then why is there so much jargon and complication involved in proving that Galilean transformations satisfy the four group properties (Closure, Associative, Identity, Inverse)? Why talk of 10 generators? Why talk of rotation as part of the proof? Can anyone point to a simple formal proof that Galilean transformations form a group, without unnecessary jargon. Once we have a simple proof that Galilean transformations form a group why can THAT not be extended to prove, in a simple way, that Lorentz transformations also form a group. Thanks.