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The outline of the proof given is nonsense. In (1): it suffices to show the existence of one normal subgroup. Proving the group abelian is unnecessary. An abelian group of this order is trivially non-simple. In (2): Sylow's Theorem doesn't say anything about the centre of a group. The orbit stabiliser formula applied to a conjugacy class gives the required result. In (3): the point here is obscured, we are constructing a homomorphism into C with a non-trivial kernal, which is then a normal subgroup, so the group is not simple. —Preceding unsigned comment added by 79.97.234.121 (talk) 08:43, 9 October 2010 (UTC)
Proof by contraposition is not mathematical induction 95.117.241.117 (talk) 23:02, 3 July 2011 (UTC)
 | This article contains a translation of Théorème de Burnside (groupe résoluble) from fr.wikipedia. (772894821 et seq.) |
I added a translation of the proof that is in the French article, except step 4 for which the French version refers to another article. Onrandom (talk) 00:18, 30 March 2017 (UTC)