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  "body": "\n## Summary\n\nA group is a set $G$ with a binary operation $\\cdot$ that has these three properties.\nThe operation is associative: $(a \\cdot b) \\cdot c = a \\cdot (b \\cdot c)$ for all $a, b, c$ in $G$.\nThere is an identity element $e$ in $G$ such that $e \\cdot a = a \\cdot e = a$ for all $a$ in $G$.\nEach element $a$ of $G$ has an inverse $a^{-1}$ in $G$ such that $a \\cdot a^{-1} = a^{-1} \\cdot a = e$.\n\nThe order of a finite group is its number of elements.\n\n## Remarks\n\n[[Lagrange's theorem|3C53TD]] gives a property of the order of a finite group.\n",
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