So I have completed a question, but I have been asked to give my answers in the form of a product of disjoint cycles. My answers are:
$$ \rho_1 = (1 4 7 6 2 5), \: \rho_2 = (1 3 7 6 2 4 5) $$
My question is, how can I possibly write these permutations as products of disjoint cycles?
Context: The question I'm answering is this,
$$ \text{Let}, \: \pi = (1 2 4 3)(5 6 7) \; \text{and} \; \sigma = (3 4 5 7)(1 2 6) \\ \text{Find an odd permutation} \; \rho_1 \; \text{and an even permutation} \; \rho_2 \; \text{such that}\\ \rho_1\pi\rho_{1}^{-1} = \rho_2\pi\rho_{2}^{-1} = \sigma $$
Community wiki answer so the question can be marked as answered:
As discussed in the comments, your results are already in the form of a product of disjoint cycles; optionally, you could add the cycle $(3)$ for the fixed point $3$ in the case of $\rho_1$.