# Computation in a Permutation Group

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 $(\tau \circ x)$.

• Please clarify the notations – Susan_Math123 Sep 5 '17 at 2:21
• Just edited the problem! – JH. Sep 5 '17 at 2:50
• 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 $\tau x$. – Stella Biderman Sep 5 '17 at 2:53
• What is $x\in X$? Is it a function? – Andrew Tawfeek Sep 5 '17 at 3:12
• What result did you get for $\sigma\circ\tau$? – bof Sep 5 '17 at 3:42