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  "body": "\n## Summary\n\nA polycyclic group is a group with a subnormal series whose factors are all cyclic.\nEquivalently, it is a solvable group in which every subgroup is finitely generated.\nPolycyclic groups form a well-behaved class of infinite groups: they are finitely presented, and many algorithmic questions about them can be decided.\n\n## Explanations\n\n### L1 human\n\nA polycyclic group is built by stacking cyclic groups one on top of another.\nEach layer is generated by a single element, so the whole group is described by finitely many elements and the way they act on each other.\nThe group $\\Z^2$ is polycyclic: the series $0 \\le \\Z \\times 0 \\le \\Z^2$ has factors $\\Z$ and $\\Z$.\nEvery finite solvable group is polycyclic, but the additive group of the rational numbers is not, since it is not finitely generated.\n",
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