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Let $\sigma , \tau \in S_3$ and $x \in X$. I need to show that for $\sigma=(1 \ 2) $ and $\tau=(2 \ 3)$, and $x = (1,2,3)$ that $(\sigma \circ \tau) \circ x \neq \sigma \circ (\tau \circ x)$. I understand how to do $(\sigma \circ \tau)$ but I don't understand how to compute the next step, or $(\tau \circ x)$.

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    $\begingroup$ Please clarify the notations $\endgroup$ – Susan_Math123 Sep 5 '17 at 2:21
  • $\begingroup$ Just edited the problem! $\endgroup$ – JH. Sep 5 '17 at 2:50
  • $\begingroup$ Can you explain in the post how to do $\sigma\tau$? I don't see how you can know how to compute that but not $\tau x$. $\endgroup$ – Stella Biderman Sep 5 '17 at 2:53
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    $\begingroup$ What is $x\in X$? Is it a function? $\endgroup$ – Andrew Tawfeek Sep 5 '17 at 3:12
  • $\begingroup$ What result did you get for $\sigma\circ\tau$? $\endgroup$ – bof Sep 5 '17 at 3:42
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It's false as permutation composition is associative

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