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  "body": "\n## Statement\n\nLet $G$ be a finite [[group|G5S1M9]] and let $g \\in G$.\nThen the [[order|0WE2NHZJ7B]] of $g$ divides the [[order|0B85S2V2DR]] $|G|$ of $G$.\n\n## Remarks\n\nThe order of $g$ is the order of the cyclic subgroup $\\langle g \\rangle$, [[by this fact|031M8HX7DA]], and [[Lagrange's theorem|3C53TD]] applies to $\\langle g \\rangle$.\nFor example, in a group of order $10$, each element has order $1, 2, 5$ or $10$.\n\n## Explanations\n\n### L1 human\n\nAn element generates a subgroup with as many elements as its order.\nThe size of a subgroup always divides the size of the group.\nSo the order of an element divides the order of the group.\n",
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