## Stable isomorphisms of groups [closed]

Possible Duplicate:
Stably isomorphic groups

If $G$ and $H$ are two groups (finitely presented, if you wish) with the property that $G\times\mathbb{Z}$ is isomorphic to $H\times\mathbb{Z}$, does that imply that $G$ is isomorphic to $H$?

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This question gets asked so often! – Steve D Apr 19 2012 at 22:45