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Well for a long time there was no proof of the Burnside theorem avoiding Representation theory. No Now there are methods to proof it without Representation theory, but they are still a lot harder then the original representation theoretic one.

http://en.wikipedia.org/wiki/Burnside_theorem

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Well for a long time there was no proof of the Burnside theorem avoiding Representation theory. No there are methods to proof it without Representation theory, but they are still a lot harder then the original representation theoretic one.

http://en.wikipedia.org/wiki/Burnside_theorem