Can Anyone prove this with words?
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a) Let = (123)(456). Find an odd permutation 2 S6 such that =.
b) Let ` be an odd integer such that ` 3. Suppose that 2 Sn, jjis odd, and
in the disjoint cycle decomposition of , there are at least twodierent cycles of
length `. Prove that there exists an odd permutation 2 Sn suchthat = .
c) Note: This part will not be marked. Do not hand in a solutionto this part.
Suppose that jj is odd, (i) = i for at most one i, and all ofthe cycles in the
disjoint cycle decomposition of have distinct lengths. Provethat there is no
odd permutation
