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.