# Math Help - cycle

1. ## cycle

Express the following permutations as the product of transpositions:

a) (1 2 3 5 7)(2 4 7 6)
b) (1 2)(1 3)(1 4)
e) (1 2 3)(3 5 7 9)(1 2 3)^-1
f) (1 2 3 4 5)^3.

Please show steps. Thanks!

2. Originally Posted by mpryal
Express the following permutations as the product of transpositions:

a) (1 2 3 5 7)(2 4 7 6)
b) (1 2)(1 3)(1 4)
e) (1 2 3)(3 5 7 9)(1 2 3)^-1
f) (1 2 3 4 5)^3.

Please show steps. Thanks!
Same approach at has down here.

You just need to know that $(a_1,a_2,...,a_k) = (a_1,a_k)...(a_1,a_3)(a_1, a_2)$

Also that $(a_1,a_2,...,a_k)^{-1} = [(a_1,a_k)...(a_1,a_3)(a_1, a_2)]^{-1} = (a_1,a_2)(a_1,a_3)....(a_1,a_k)$

And for $(12345)^3$ just imagine $(12345)(12345)(12345)$.

Show you work.