... 〈·, ·〉. If X is a vector field on G such that 〈·, ·〉 is m-quasi-Einstein for m finite, i.e. RicmX = λ〈·, ·〉, then X is a left-invariant Killing field. Theorem 1.1 for compact Lie groups is proved in =-=[CL13]-=-, and there are non-trivial m-quasi-Einstein metrics on homogeneous manifolds [BRJ12, CL13]. Furthermore, we will prove that Theorem 1.1 for m infinite fails for solvable quadratic Lie groups. It is d...