A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series g^1 = [g, g], g^2 = [g^1, g^1], ... eventually vanishes, g^k = 0 for some k. Since nilpotent Lie algebras are also solvable, any nilpotent Lie group is a solvable Lie group.
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