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