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Jul 24, 2015 at 13:33 comment added Jason Starr Presumably your argument also establishes the case when $G$ is residually finite. Of course there are finitely presented, infinite, simple groups . . .
Jul 23, 2015 at 20:31 comment added KotelKanim This is good news, but actually I am interested in the infinite (finitely presented) case.
Jul 23, 2015 at 17:10 history answered Alex B. CC BY-SA 3.0