What is $(1372)(56) \circ(154)$ and how to work out similar compositions?
What is $(1372)(56) \circ (154)$ and how to work out similar compositions?
1
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group-theory
permutations
1 Answers
1
Start with $1,$ and work from right to left.
the first (right most) cycle takes $1$ to $5$ And the next takes it to $6.$
We write $(16\cdots$
Now we look to see where $6$ goes. the first cycle does nothing to it, and the second takes it to $5$
$(165\cdots$
And now do the same for $5.$ Eventually you get something that takes you back to 1. When you get there, close the cycle.
Has everything been mapped? If not, what is the smallest number not accounted for. Find the disjoint cycle that starts here.
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0It should be pointed out that which cycle is first depends on convention. If your permutations are acting on the left (like functions as they're usually taught) then this answer is perfect, but many people do have permutations act on the right - in this case the first cycle is the left most. – 2017-01-26