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Question 1205220: Determine the order of the following elements.
a) [1 2 3 4 5 2 3 4 5 1]
b) [1 2 3 4 4 3 1 2 ]
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To determine the order of a permutation, we need to find the smallest positive integer k such that the permutation raised to the power of k equals the identity permutation.
**a) [1 2 3 4 5 2 3 4 5 1]**
This permutation can be written in cycle notation as (1 2 3 4 5).
* Applying this permutation 5 times, we get back to the original order.
* Therefore, the order of this permutation is 5.
**b) [1 2 3 4 4 3 1 2 ]**
This permutation can be written in cycle notation as (1 2)(3 4).
* Applying (1 2) twice, we get back to the original order.
* Similarly, applying (3 4) twice, we get back to the original order.
* The least common multiple of 2 and 2 is 2.
* Therefore, the order of this permutation is 2.
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