1) Consider a = (123)(456). Determine the odd permutation b in S6 such that ab = ba.
2) Consider l be the odd integer such that l >= 3. Assume that a is in Sn, |a| is odd and in disjoint cycle decomposition of the a, there are at least 2 different cycles of given length l. Verify that there exists odd permutation b in Sn such that ab = ba.