The two-line symbols for permutations p and q in S_5 are p = (1 2 3 4 5 3 4 5 2

Question

The two-line symbols for permutations p and q in S_5 are p = (1 2 3 4 5 3 4 5 2 1) and q = (1 2 3 4 5 2 4 3 5 1) Write down the permutations p, q, p^-1 and q^-1 in cycle form. Determine the permutations po q and q o p in cycle form, and write down the orders of p, q, p o q and q o p. Write p and q as composites of transpositions, and state the parity of p and of q. Let r be the permutation in S_5 whose cycle form is (2 3 4). Find, in cycle form, the permutation s = r o p o r^-1, that is, the conjugate of p by r. Determine, in cycle form, the elements of the cyclic subgroup of S_5 generated by p.

Explanation / Answer

The two-line symbols for permutations p and q in S_5 are p = (1 2 3 4 5 3 4 5 2

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