On the Poincar\'e Group and the Poincar\'e Group Derivative

The Poincar\'e Group is a group of symmetric groups that are not of the Poincar\'e Group. The Poincar\'e Group Derivative is a group of groups with all symmetries considered. The Poincar\'e Group Derivative is itself a Poincar\'e Group. We investigate the Poincar\'e Group Derivative in the context of the Poincar\'e Group and the Poincar\'e Group Derivative. We construct and calculate the Poincar\'e Group Derivative of the Poincar\'e Group and the Poincar\'e Group Derivative, and prove that the Poincar\'e Group Derivative is a Poincar\'e Group. We argue that the Poincar\'e Group Derivative is a Poincar\'e Group.