1. The problem statement, all variables and given/known data Suppose G and F are groups and GxF is isomorphic to G'xF', if G is isomorphic to G', can we conclude that F is isomorphic to F'? 2. Relevant equations 3. The attempt at a solution I'm trying to give a proof using the first isomorphism theorem (using that GxF/Gx(e) is isomorphic to F, and that G'xF'/G'x(e) is isomorphic to F'), but I can't find an isomorphism between the quotients. I also can't find a counter example of the statement, so any help or suggestions would be appreciated.