Can all connected locally compact groups be written as a product of abelian and compact subgroups?

Question

Is it true that given a connected locally compact group $G$, there must be abelian subgroups $H_{1},\dots, H_{n}$ and a compact subgroup $K$ of $G$ such that $G$ is homeomorphic to $H_{1}\times H_{2}\times\cdots\times H_{n}\times K$?

If so, can anyone supply a reference?

Any response is greatly appreciated!