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So I know that $A_5$ is not solvable but I don't know how to go about showing that other groups can't be solvable. I think that this theorem might be useful but I haven't found a smart way to use it. Thm: A group G is solvable iff $G^{(n)}=\{1\}$ for some n

McNuggets666
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  • I would think the Sylow theorems are helpful at least in excluding a lot of different possible orders. But I don't know a good general proof. – Arthur Dec 04 '16 at 18:17
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    Do you know Burnside theorem https://en.wikipedia.org/wiki/Burnside_theorem? –  Dec 04 '16 at 18:21
  • Also look at http://math.stackexchange.com/questions/413056/question-about-solvable-groups/413612#413612 –  Dec 04 '16 at 18:25

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