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We know that if there exists an element of a given order in a group, there also exists a cyclic subgroup of that order. What about converse?

Suppose there is a subgroup of an Abelian group of order 'm'. Does that imply there also exists an element of order 'm' in the Group. It does not hold in general for Non-Abelian groups. But what about Abelian groups?

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# Subgroup of given order of an Abelian group

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