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  "body": "\n## Summary\n\nA subset $S$ of a [[group|G5S1M9]] $G$ generates $G$ when the [[subgroup generated by $S$|0RP7VWQ0YN]] is all of $G$.\nThen each element of $G$ is a finite product of elements of $S$ and of their inverses. The elements of $S$ are called generators of $G$.\n\n## Remarks\n\nThe set $\\{1\\}$ generates $(\\mathbb{Z}, +)$, and so does the set $\\{2, 3\\}$.\nEach group is generated by the set of all its elements.\nA group generated by one element is a cyclic group, and a group generated by a finite set is a finitely generated group.\n\n## Explanations\n\n### L1 human\n\nGenerators are building blocks for a group: you can reach each element from them with products and inverses.\nA small set of generators gives a short description of a big group.\nFor example, all symmetries of a square come from one rotation and one reflection.\n",
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