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