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Lagrange's theorem (Theorem)

Let $ G$ be a finite group and let $ H$ be a subgroup of $ G$. Then the order of $ H$ divides the order of $ G$.



"Lagrange's theorem" is owned by Evandar.
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See Also: group, proof of Fermat's little theorem using Lagrange's theorem, proof of Euler-Fermat theorem using Lagrange's theorem


Attachments:
proof of Lagrange's theorem (Proof) by akrowne
proof of the converse of Lagrange's theorem for finite cyclic groups (Proof) by Wkbj79
proof that every group of prime order is cyclic (Proof) by Wkbj79
calculus of subgroup orders (Application) by Algeboy
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Cross-references: divides, order, subgroup, finite group
There are 17 references to this entry.

This is version 2 of Lagrange's theorem, born on 2002-01-23, modified 2002-02-02.
Object id is 1566, canonical name is LagrangesTheorem.
Accessed 14733 times total.

Classification:
AMS MSC: 20D99 (Group theory and generalizations :: Abstract finite groups :: Miscellaneous)
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