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- Thread starter Pjennings
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- #2

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Have they not gone through Lagrange's theorem yet?

- #3

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Who said any of the groups were finite?Have they not gone through Lagrange's theorem yet?

- #4

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good point.Who said any of the groups were finite?

- #5

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Of course, it's not hard to just count the number of cosets. G = g_1K + ... + g_nK where n = [G:K]. K = k_1H + ... + k_mH, where m = [H:K]. Then G = g_1(k_1 + ... + k_m)H + ... + g_n(k_1+...+k_m)H, where I have abused notation a little. This shows [G]<=[G:K][K]. Now think about the other direction.

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