I am trying to compute a permutation: $\alpha = (13)(246)$ and $\beta = (1524)$. Find $\alpha\beta$. I thought that I had a good grasp on these, but I checked it on a site, and if it is correct, I am wrong and I can't figure out how to make sense of their answer.
I got $\alpha\beta$ = (1543)(26)
Their answer = (1352)(46).
Can anyone give me direction on this?
Those permutations are bijections $S\to S$ where $S=\{1, 2, 3, 4, 5, 6\}$, and $\alpha\beta = \alpha\circ\beta$. Using what we know, we have $(\alpha\circ\beta)(1)=\alpha(5)=5, (\alpha\circ\beta)(2)=\alpha(4)=6, (\alpha\circ\beta)(3)=\alpha(3)=1, (\alpha\circ\beta)(4)=\alpha(1)=3, (\alpha\circ\beta)(5)=\alpha(2)=4, (\alpha\circ\beta)(6)=\alpha(6)=2$. Thus, 1 goes to 5, 5 goes to 4, 4 goes to 3, 3 goes to 1 (giving you (1543)), and 2 goes to 6, 6 goes to 2 (giving (26)).