PlanetMath: Cauchy's theorem

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Cauchy's theorem

(Theorem)

Let be a finite group and let be a prime dividing $\vert G\vert$ . Then there is an element of of order .

"Cauchy's theorem" is owned by Evandar.

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Attachments:: proof of Cauchy's theorem (Proof) by yark
proof of Cauchy's theorem in abelian case (Proof) by kshum

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Cross-references: order, prime, finite group
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This is version 1 of Cauchy's theorem, born on 2002-01-23, modified 2002-02-01.
Object id is 1569, canonical name is CauchysTheoremForFiniteGroups.
Accessed 9102 times total.

Classification:

AMS MSC:	20D99 (Group theory and generalizations :: Abstract finite groups :: Miscellaneous)
	20E07 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Subgroup theorems; subgroup growth)

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