Chapter 4.1, Problem 13E

Exercises

For the given permutations, $f$ and $h$, find a permutation $g$ such that $h$ is the conjugate of $f$ by $g$ –that is, such that $h=gf{g}^{-1}$.

a. $f=(1,5,9)$; $h=(2,6,4)$

b. $f=(1,3,5,7)$; $h=(3,4,6,8)$

c. $f=(1,3,5)(2,4)$; $h=(2,4,3)(1,5)$

d. $f=(1,2,3)(4,5)$; $h=(2,3,4)(1,6)$

e. $f=(1,4,7)(2,5,8)$; $h=(1,5,4)(2,3,6)$

f. $f=(1,3,5)(2,4,6)$; $h=(1,2,4)(3,5,6)$