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Feb 7, 2010 at 17:48 comment added gowers I don't claim it's a good way of doing things, but one could (in desperation) argue that here one is defining quotients in just one situation (what you need to define a group in terms of generators and relations) and getting all quotients out of it. But I wouldn't want to go to the wall on this one ...
Feb 7, 2010 at 16:41 comment added Martin Brandenburg "it might end up being an unnecessarily complicated way of presenting essentially the same proof." unfortunately, yes. besides you also use quotients (by identifying things) in this construction.
Feb 7, 2010 at 16:38 history answered gowers CC BY-SA 2.5