PlanetMath: Lagrange's theorem

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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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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
subgroups with coprime orders (Theorem) by pahio

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Cross-references: divides, order, subgroup, finite group
There are 19 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 18285 times total.

Classification:

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

Pending Errata and Addenda

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