We know that all locally compact abelian groups are isomorphic to groups of the form $R^n \times H$ where H is a locally compact abelian group that contains an open compact subgroup K. Furthermore, every compactly generated locally compact abelian group is isomorphic to a group of the form $R^n \times Z^m \times K$ for some compact group K. Are there any similar results if we drop commutativity?