How to multiply permutations together?

Question

This is straight from an exam question: Find the order of the permutation $(1465732)(358)(79)$ in $S_9$

So I understand that I first have to write this permutation in disjoint cycle notation, but I'm having trouble doing so. For example if you look at 3, (going from right to left) we have

$ 3 \to 5 $, $ 5\to 7$ so in effect $3 \to 7$

But then we also have from the first cycle $3 \to 2$?

So where is 3 actually sent by this composition of permutations? Thanks.

Your first part was correct. The $3\to 2$ part will only have effect on some element sent to $3$ by the previous cycles. — Tobias Kildetoft, Apr 20 '15 at 12:11

score 4 · Accepted Answer · answered Apr 20 '15 at 12:16

4

Just recall that the product of these cycles is just composition of maps. So if you apply your permutation $(1465732)(358)(79)$ to $3$ you will have $$ (1465732) \circ (358) \circ (79) \ 3 = (1465732) \circ (358) \ 3 = (1465732) \ 5 = 7. $$

answered Apr 20 '15 at 12:16

Andreas Caranti

70,862

How to multiply permutations together?

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