📐 Lagrange

If $H \\leq G$ and $G$ is finite, then $|H|$ divides $|G|$. The index is $[G:H] = |G|/|H|$.

Proof: Cosets partition $G$ into $[G:H]$ sets, each of size $|H|$. Thus $|G| = [G:H] \\cdot |H|$.

From: intro-discrete

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