Disjoint cycles and least common multiple

Reference no: EM13125743

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?

Reference no: EM13125743

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