Find $\sigma$ in $S_5$ that fulfills: $$\sigma(12)(34)=\sigma^{-1}(13)(45)$$ Can anyone help with that? i've tried to multiply by $\sigma^{-1}$ from the right side but it doesn't seem to lead anywhere
Symmetric groups
0
$\begingroup$
group-theory
permutations
symmetric-groups
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1Try multiplying by $\sigma$ on the left and $(12)(34)$ on the right. – 2017-01-31
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1why does a $5$ appear there? – 2017-01-31
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0@JorgeFernándezHidalgo Heh, good catch. – 2017-01-31
1 Answers
2
You need $\sigma^2=(13)(45)(12)(34)=(12354)$ Clearly $\sigma$ must be a $5$-cycle also, so we get $\sigma=\sigma^6=(12354)^3=(15243)$