
> 
> **Possible Duplicate:**  
> 
> [Stably isomorphic groups](https://mathoverflow.net/questions/33589/stably-isomorphic-groups) 
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> 
> 


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 $H$?



Stable isomorphisms of groups
See [Stably isomorphic groups](https://mathoverflow.net/questions/33589/stably-isomorphic-groups) (Hirshon's example is finitely presented). 


