# Check that the Poincaré's transformations form a group structure

How can I answer to this question ? I know that this is a Lorentz transformation + a translation but I don't know how to start. What's the difference between group/group structure ?

• Saying that something has a "group structure" just means that it satisfies the "group axioms", which also means that it is a group. So you answer this question by looking at the group axioms, and showing that they all apply to your group. Maybe start with just the translations, and move on once you get the idea of how this works. For example, you know that there's an identity element (the translation by zero), each element has an inverse (translation by the same amount in the opposite direction), ... – Mike Feb 20 at 17:21
• ... if you combine two translations you get another translation (you could probably show this using vectors), and translations combine associatively (again, use vectors). You'll need to work a little harder to incorporate rotations and boosts, but that's the basic idea. – Mike Feb 20 at 17:24