Unsolvable series
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Find the derived series for S_4
Show that S'_n=A_n if n is not equal to 2 and conclude that S_n is not solvable if n is greater than or equal to 5.
I need a detailed proof of this to study please.
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Solution Summary
This provides an example of concluding a series is not solvable.
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We have
S_4 > A_4 > (A_4)' = { double transpositions } > {( )}
If n = 2, [S_n, S_n] = { ( ) } = A_n.
Consider n > 2, and let a = (1 2) and b = (1 2 3); then
aba^{-1} b^{-1} = (1 ...
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