91Ó°ÊÓ

In Exercises 1 through 6, find all orbits of the given permutation. $$ \left(\begin{array}{llllll} 1 & 2 & 3 & 4 & 5 & 6 \\ 5 & 1 & 3 & 6 & 2 & 4 \end{array}\right) $$

In Exercises 1 through 6, find all orbits of the given permutation. $$ \left(\begin{array}{llllllll} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 5 & 6 & 2 & 4 & 8 & 3 & 1 & 7 \end{array}\right) $$

In Exercises 1 through 6, find all orbits of the given permutation. $$ \left(\begin{array}{llllllll} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 2 & 3 & 5 & 1 & 4 & 6 & 8 & 7 \end{array}\right) $$

In Exercises 1 through 6, find all orbits of the given permutation. $$ \sigma: \mathbb{Z} \rightarrow \mathbb{Z} \text { where } \sigma(n)=n+1 $$

In Exercises I throngh 6 . find all orbits of the given permutation. \(\sigma: \mathrm{Z} \rightarrow \mathrm{Z}\) where \(\sigma(n)=n+2\)

In Exercises 1 through 6, find all orbits of the given permutation. $$ \sigma: \mathbb{Z} \rightarrow \mathbb{Z} \text { where } \sigma(n)=n+2 $$

In Exercises 1 through 6, find all orbits of the given permutation. $$ \alpha: \mathbb{Z} \rightarrow \mathbb{Z} \text { where } \sigma(n)=n-3 $$

In Exercises 7 through 9 , compute the indicated product of cycles that are permutations of \(\\{1,2,3,4,5,6,7,8\\}\). $$ (1.4,5)(7,8)(2,5,7) $$

In Exercises 7 through 9 , compute the indicated product of cycles that are permutations of \(\\{1,2,3,4,5,6,7,8\\}\). $$ (1,3,2,7)(4,8,6) $$

In Exercises 7 through 9 , compute the indicated product of cycles that are permutations of \(\\{1,2,3,4,5,6,7,8\\}\). $$ (1.2)(4,7,8)(2,1)(7,2,8,1,5) $$