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 $H$?
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 $H$? 

marked as duplicate by Benjamin Steinberg, S. Carnahan♦ Apr 20 '12 at 3:13This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 


See Stably isomorphic groups (Hirshon's example is finitely presented). 

