Question

Find the order of each permutation.

(d)$\left(1234\right)\left(4231\right)$

Short answer

The order of a permutation$\left(1234\right)\left(4231\right)$ is 3.

Step-by-step solution

Order of a permutation

Theorder of a permutation $\sigma$ is the smallest positive integer$n$ such that ${\sigma }^n=\in$, where$\in$ is the identity permutation.

Permutation σ2 and σ3

Apply the permutation $\sigma$twice. Then,

Now, apply the permutation $\sigma$thrice. Then,

Here, n = 3 is the smallest positive integer such that${\sigma }^3=\in$

Therefore, the order of a permutation$\left(1234\right)\left(4231\right)$is 3.