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An element of a finite group

by llauren84
Tags: element, finite
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llauren84
#1
Dec15-12, 12:27 AM
P: 44
I need help with this theorum, please.

How is this (the attachment) true? It's for my cryptology class.

The rest of the day's notes are here: http://crypto.linuxism.com/thursday_december_13_2012
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Number Nine
#2
Dec15-12, 02:19 AM
P: 772
You might try applying Lagrange's theorem; that should set you in the right direction.
Stephen Tashi
#3
Dec15-12, 02:30 AM
Sci Advisor
P: 3,245
If [itex] G [/itex] is a finite group with order [itex] |G| [/itex] then for each element [itex] a \in G [/itex] , [itex] a^{|G]} = I [/itex], the identity.
Are you asking how to write a proof of the theorem or for some intuitive indication why it is true?

llauren84
#4
Dec15-12, 03:58 AM
P: 44
An element of a finite group

LaGrange's theory helped thanks. Also, the rewritten form of the statement helped, so thanks both of you.


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