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  "body": "\n## Summary\n\nThe upper central series of a group $G$ is the sequence $\\{e\\} = Z_0 \\subseteq Z_1 \\subseteq Z_2 \\subseteq \\cdots$, where $Z_1$ is the centre and $Z_{i+1}/Z_i$ is the centre of $G/Z_i$.\nThe group is nilpotent if and only if this series reaches $G$.\n",
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