Question: Please help with with the following two questions. This is the chapter of Lagranges Theorem. Please show step by step and give a good expiation

Please help with with the following two questions. This is the chapter of Lagranges Theorem. Please show step by step and give a good expiation please.

11.9. Let G be a finite abelian group and let m be the least common multiple of the orders of its elements. Prove that G contains an element of order m. 11.10. Supply a finite non-abelian group for which the conclusion of the previous exercise fails

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