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text: 'Lagrange's Theorem states that if $G$ is a finite [-3gd] and $H$ a subgroup, then the [3gg order] $|H|$ of $H$ divides the order $|G|$ of $G$.\nIt generalises to infinite groups: the statement then becomes that the [4j4 left cosets] form a [set_partition partition], and for any pair of cosets, there is a [499 bijection] between them.\n\n# Proof\n\nIn full generality, the cosets [4j5 form a partition] and [4j8 are all in bijection].\n\nTo specialise this to the finite case, we have divided the $|G|$ elements of $G$ into buckets of size $|H|$ (namely, the cosets), so $|G|/|H|$ must in particular be an integer.',
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