Let $\sigma =(a_1...a_6)$ be a $6$-cycle. Write the disjoint cycle decomposition of $\sigma^2$ and $\sigma^3$.
I know that $a_1*a_1=\epsilon $ but does this mean that $\sigma^2=\epsilon$ and then $\sigma^2=\sigma$ ?
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How do you know that $a_1a_2=\epsilon$? What does that even mean? What is $a_1$ and what does $$ mean? – bof Feb 09 '16 at 23:22
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1Have you tried actually writing out $\sigma^2$ and $\sigma^3$? – rogerl Feb 09 '16 at 23:27
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I've tried to write it out, I'm not sure if I'm multiplying? in the write way though. – Alex Feb 09 '16 at 23:40
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Do it first for $\sigma=(123456)$. – lhf Feb 09 '16 at 23:45
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would that mean σ2=(135)(246) (sorry about the notation! I'm new and not good with that stuff yet) – Alex Feb 09 '16 at 23:49