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  "body": "\n## Definition\n\nAn abelian group is a [[group|G5S1M9]] $(G, \\ast)$ whose operation is [[commutative|099E72KTF8]].\nThus $a \\ast b = b \\ast a$ for all $a, b \\in G$.\n\n## Remarks\n\nThe integers, the rationals and the real numbers with addition are abelian groups.\nThe operation of an abelian group is often written $+$, with identity $0$ and inverse $-a$.\nThe group of invertible $2 \\times 2$ real matrices under multiplication is not abelian.\n\n## Explanations\n\n### L1 human\n\nIn an abelian group, the order of two elements in a product does not matter.\nAddition of numbers is the model: $a + b = b + a$.\nThe name honours Niels Henrik Abel.\n",
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