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Let $\sigma$ be the permutation:

$$\begin{array} {}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 3 & 5 & 6 & 2 & 4 & 9 & 8 & 7 & 1, \end{array}$$ $I$ be the identity permutation and $m$ be the order of $\sigma$ i.e. $m=\text{min}\{\text{positive integers }n: \sigma ^n=I \}$. Then $m$ is

  1. $8$
  2. $12$
  3. $360$
  4. $2520$
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1 Answer

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Disjoint cycles are (1,3,6,9),(2,5,4),(7,8)

length of them are respectively : { 4,3,2}

so m is lcm(4,3,2) = 12
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