How Does an Element of a Finite Group Relate to Cryptology Theorems?

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    Element Finite Group
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Discussion Overview

The discussion revolves around the relationship between elements of finite groups and cryptology theorems, specifically focusing on a theorem relevant to a cryptology class. Participants explore theoretical aspects and seek clarification on the theorem's validity.

Discussion Character

  • Homework-related, Technical explanation

Main Points Raised

  • One participant requests help with a theorem related to cryptology, indicating uncertainty about its truth.
  • Another participant suggests applying Lagrange's theorem as a potential approach to understanding the problem.
  • A third participant states a property of finite groups, mentioning that for any element in a finite group, raising it to the order of the group yields the identity element.
  • The initial requester acknowledges that Lagrange's theorem and a rewritten form of the statement provided clarity.

Areas of Agreement / Disagreement

Participants do not express any disagreement, but the initial request for help indicates uncertainty about the theorem's validity. The discussion remains focused on exploring the theorem without reaching a consensus on its implications.

Contextual Notes

The discussion does not clarify the specific theorem in question, nor does it address any assumptions or definitions that may be necessary for a complete understanding.

llauren84
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You might try applying Lagrange's theorem; that should set you in the right direction.
 
If G is a finite group with order |G| then for each element a \in G , a^{|G]} = I, the identity.

Are you asking how to write a proof of the theorem or for some intuitive indication why it is true?
 
LaGrange's theory helped thanks. Also, the rewritten form of the statement helped, so thanks both of you.
 
Last edited:

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