Abstract Algebra/Group Theory/Subgroup/Lagrange's Theorem

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Theorem[edit | edit source]

Let H be a subgroup of group G.

Let o(H), o(G), be orders of H, G respectively

o(H) divides o(G)

Proof[edit | edit source]

As H is Subgroup of G,

1. All Left Cosets of H partitions G.
2. Each of such partitions is one of the Cosets of H.
3. Any coset of H has the same order as H does.
4. Thus, o(H) divides o(G)