# Permutation Group

1. Sep 3, 2010

### roam

1. The problem statement, all variables and given/known data

I have problems understanding part (f) of the following worked example:

[PLAIN]http://img7.imageshack.us/img7/5557/61793282.gif [Broken]

3. The attempt at a solution

So in part (f), when calculating $$(\sigma \tau)^{9000}$$, how does $$(\sigma \tau)^{818 \times 11} (\sigma \tau)^2$$ reduce to $$(\sigma \tau)^2$$? What happens to the $$(\sigma \tau)^{818 \times 11}$$ part?

Similarly in $$(\sigma \tau)^{-21}=(\sigma \tau)^{-2 \times 11} (\sigma \tau)^1 = (\sigma \tau)^1$$

why has the "$$(\sigma \tau)^{-2 \times 11}$$" been omitted?

Last edited by a moderator: May 4, 2017
2. Sep 3, 2010

### Office_Shredder

Staff Emeritus
What is $$(\sigma \tau)^11$$ equal to? Hint: You know that it has order 11

3. Sep 6, 2010

### roam

Well, $$(\sigma \tau)^{11}=e$$ where e is the identity. But what happens to the $$(\sigma \tau)^{-2}$$? Why does the "-2" disappear (since anything multiplied by the identity is itself)?

4. Sep 6, 2010

### Office_Shredder

Staff Emeritus
$$(\sigma \tau)^{-2 \times 11} = ((\sigma \tau)^{11})^{-2}$$