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gtfitzpatrick
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Homework Statement
show that if ##(x_1 x_2 ... x_k)## is a cycle in ##S_n## ( ##k \leq n## ) and ##\pi## is any permutation in ##S_n## then ##\pi (x_1 x_2 ... x_k) \pi ^{-1} = ( \pi(x_1) \pi(x_2) ... \pi(x_k) )##
Homework Equations
The Attempt at a Solution
firstly is this question right?
i multiplied both sides by ##\pi^{-1}## and get
[tex](x_1 x_2 ...x_k)\pi^{-1} = \pi^{-1} (\pi(x_1) \pi(x_2) ...\pi(x_k))[/tex]
[tex] = \pi^{-1}\pi(x_1) \pi^{-1}\pi(x_2) ...\pi^{-1}\pi*x_k)) [/tex]
[tex]=(x_1 x_2 ... x_k)[/tex]
which obviously isn't right?
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