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May 22, 2013 at 17:01 comment added Matt Brin I now understand my confusion and my second error. Gerry is right since he interpreted my notation literally and I did not. In [X,X], I erred in letting the elements run over X and also the inverses of elements in X.
May 22, 2013 at 8:04 comment added user6976 @Alireza: Isn't it what Matt wrote in his comment to Gerry's answer. I think the only non-clear remaining part of the question is whether $X_2=1$ implies $G_m=1$ for some $m$.
May 21, 2013 at 13:28 history answered Alireza Abdollahi CC BY-SA 3.0