The order of an element in a finite group divides the order of the group ↩

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created: 2021-12-06 13:03:25
modified: 2022-01-10 04:13:04

Statement: finite group, .
Then the order of divides the order of the group, .

Proof

Since the cycle generated by the element is a subgroup itself, and the order of a subgroup divides the order of the group.