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Let $f, g \in S_n$
I am to proof the following theorem: $$sgn(f\circ g) = sgn(f)\cdot sgn(g)$$ What I know is that $$sgn(f) = (-1)^{I(f)}$$ Where $I(f)$ is the number of transposition in permutation $f$.
However I don't know how can the proof should look like.

Hendrra
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  • Hint: write $f$ and $g$ as products of transpositions. Then write $f \circ g$ as a product of transpositions. – kccu Apr 26 '17 at 21:56
  • I thought about that. But I'm not sure how can I do that @kccu – Hendrra Apr 26 '17 at 22:00
  • Well you know that $f$ and $g$ can be written as products of transpositions, right? So suppose $f=\tau_1\cdots \tau_m$ and $g=\sigma_1\cdots \sigma_n$ where $\tau_i$ and $\sigma_i$ are transpositions. Do you see where to go from there? – kccu Apr 26 '17 at 22:02

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