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  3. a symmetric group s5 acts on the set x5 = {(i, j)

a symmetric group S5 acts on the set X5 = {(i, j) : i, j...

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Advance Math

a symmetric group S5 acts on the set X5 = {(i, j) : i, j ? {1,2, 3, 4, 5}}.

S5 will also act on this set. Consider the subgroup H = <(1,2)(3, 4), (1, 3)(2, 4)>? S5. (a) Find the orbits of H in thisaction. Justify your answers. (b)

For each orbit find the stabiliser one of its members. Justifyyour answers.

action is this t.(i,j)=(t(i),t(j))

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