QUESTION
Suppose that α, β are disjoint cycles in the symmetric group Sm for m ≥ 9.
a) Let α by a cycle of length 3 and β a cycle of length 9. What is the order of αβ. Is the permutation αβ even or odd?
b/ Show that for every positive integer n we have (αβ)raised to the power n = α raised to the power n times β raised to the power n
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