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!

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- Apr 24th 2009, 07:47 AMmpryalcycle decomposition 3
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! - Apr 24th 2009, 08:56 AMThePerfectHacker
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.