Symmetric groups: G = Sn.
(i) Let g1, g2 belong G be two disjoint cycles, and let g = g1g2. Prove that o(g) = lcm
{ o( g1), o(g2)}, where lcm stands for the least common multiple.
(ii) Let g= g1g2 ... gr belong G, where g1,g2, ... gr are disjoint cycles. Prove that o(g) = lcm {o(g1), o(g2), ... o(gr)}.
Can you tell me how to start, and step by step guide?