Linear Algebra and Its Applications vol:359 pages:101-111
Let G be a 2-step nilpotent Lie group with a 1-dimensional commutator subgroup. We prove that for any simply transitive and affine action of G, there exists a non-trivial subgroup of G acting as pure translations. This result no longer holds in case the commutator subgroup is higher dimensional. (C) 2002 Elsevier Science Inc. All rights reserved.