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  "body": "\n## Summary\n\nIn abstract algebra, an [[abelian group|071DDFVG4J]] $(G,+)$ is called finitely generated if there exist finitely many elements $x_1,\\dots,x_s$ in $G$ such that every $x$ in $G$ can be written in the form $x = n_1x_1 + n_2x_2 + \\cdots + n_sx_s$ for some [[integers|0C4JS9RF5M]] $n_1,\\dots, n_s$. In this case, we say that the set $\\{x_1,\\dots, x_s\\}$ is a *[[generating set|0MBV2VHMXA]]* of $G$ or that $x_1,\\dots, x_s$ *generate* $G$. So, finitely generated abelian groups can be thought of as a generalization of cyclic groups.\n",
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