Chapter 4.1, Problem 4E

In each part of Exercise $2$, decide whether the permutation is even or odd.

Express each permutation as a product of disjoint cycles and find the orbits of each permutation.

a. $(1,9,2,3)(1,9,6,5)(1,4,8,7)$

b. $(1,2,9)(3,4)(5,6,7,8,9)(4,9)$

c. $(1,4,8,7)(1,9,6,5)(1,5,3,2,\text{}9)$

d. $(1,4,2,3,5)(1,3,4,5)$

e. $(1,3,5,4,2)(1,4,3,5)$

f. $(1,9,2,4)(1,7,6,5,9)(1,2,3,8)$

g. $(2,3,7)(1,2)(3,5,7,6,4)(1,4)$

h. $(4,9,6,7,8)(2,6,4)(1,8,7)(3,5)$