Express as the product of disjoint cycles and find the order.
a) (1 2 3 5 7)(2 4 7 6)
b) (1 2)(1 3)(1 4)
e) (1 2 3)(3 5 7 9)(1 2 3)^-1
f) (1 2 3 4 5)^3.
Please show steps. Thanks!
If a permutation is expressed as a product of disjoint cycles then the order is the lowest common multiple of all the cycle lengths. This permutation is not a product of disjoint cycles, so we have to turn it into a product of disjoint cycles.
Note (under this permutation):
Thus,
This means the order is
Try the other ones and show your work.