This stabilization assembly comprises a solid cage body (1) designed to be introduced by impaction into the intervertebral space (E), and a nose (36) for introducing the cage body into the intervertebral space, this nose being integrally connected or being able to be integrally connected to this cage body in an eccentric position in such a way that, when this nose is introduced into the intervertebral space, the rotation of this nose induces an opening of this intervertebral space and, simultaneously, a displacement of the cage body in the manner of a cam.