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 $\displaystyle (a_1,a_2,...,a_k) = (a_1,a_k)...(a_1,a_3)(a_1, a_2)$
Also that $\displaystyle (a_1,a_2,...,a_k)^{-1} = [(a_1,a_k)...(a_1,a_3)(a_1, a_2)]^{-1} = (a_1,a_2)(a_1,a_3)....(a_1,a_k)$
And for $\displaystyle (12345)^3$ just imagine $\displaystyle (12345)(12345)(12345)$.
Show you work.