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Given f=(1,2)(3,4),(5,4) g=(2,3)(4,3),(6,1)

User Ideamotor
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The composition of permutations g∘f is achieved by applying f followed by g. The resulting permutation, expressed as a single cycle notation, is (1 6)(2 3 4 2)(5).

The composition g∘f is found by applying f first and then g. Let's calculate:

f = (1,2)(3,4)(5,4)

g = (2,3)(4,3)(6,1)

Applying f to each element:

f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 5, f(5) = 1

Now, applying g to the result:

g(2) = 3, g(3) = 4, g(4) = 2, g(5) = 1, g(1) = 6

Combining these results into a single cycle notation:

g∘f = (1 6)(2 3 4 2)(5)

So, the composition g∘f expressed as a single cycle notation is (1 6)(2 3 4 2)(5).

Complete question:

Given f=(1,2)(3,4),(5,4) and g=(2,3)(4,3),(6,1), determine the composition g∘f and express the result as a single cycle notation.

User Mario Petrovic
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