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  "body": "\n## Summary\n\nA torsion group, also called a periodic group, is a [[group|G5S1M9]] in which every element has finite [[order|0WE2NHZJ7B]].\nEvery finite group is a torsion group, but there are also infinite ones.\nThe Burnside problem asks whether a finitely generated torsion group must be finite; the answer is no in general.\nFor an abelian group, the elements of finite order form the [[torsion subgroup|0DBWXQRXQJ]].\n\n## Explanations\n\n### L1 human\n\nIn a torsion group, if you take any element and multiply it by itself again and again, you come back to the identity after finitely many steps.\nA clock is a good picture: adding hours, you always return to 12.\nThe group $\\Q/\\Z$ of fractions modulo $1$ is an infinite example.\nThe fraction $\\tfrac{3}{7}$ added to itself $7$ times gives $3$, which is $0$ modulo $1$.\nThe integers are not a torsion group, because adding $1$ to itself never returns to $0$.\n",
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