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

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 this action. Justify your answers. (b)

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

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

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Expert Solution

Colby Messinger answered 1 year ago

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