3. Let a and ẞ be permutations in S11 with a = (7 4 1 3) (28) (5) (9 6 10 11), β = ( 1 2 3 8 7 10 4 5 6 1 6 7 8 9 10 11 5 11 4 239 (a) Express ẞ as a composition of disjoint cycles. (b) Find the fixed points of ẞ². (c) Express a oẞ as a composition of disjoint cycles. (d) Find the orders of a and B. [1] [1] [1] [2] (e) Determine whether a is an even or odd permutation, explaining your rea- soning clearly. [2] (f) Find S11 such that Boy = a, showing your reasoning clearly. [3]

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