Clearification about order of groups

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Homework Help Overview

The discussion revolves around group theory, specifically the properties of groups with prime order and their isomorphism to cyclic groups.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • The original poster seeks clarification on whether a group of prime order is always isomorphic to the cyclic group of the same order. Some participants affirm this and suggest exploring isomorphisms between groups of prime order.

Discussion Status

The discussion includes affirmations of the original poster's question, with some participants encouraging further exploration of isomorphisms to deepen understanding. There is no explicit consensus, but a productive direction is suggested.

Contextual Notes

Participants are discussing the implications of group order and isomorphism without delving into specific examples or proofs.

spacenerd
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When a group has a prime order, does that mean that it is always isomorphic to the cyclic group of the same order? I just am a little confused and need some clarification on this matter.
Thanks
 
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Yes! If a group has a prime order p, then the group has to be isomorphic to [tex]\mathbb{Z}_p[/tex]!
 
Thanks :)
 
spacenerd said:
Thanks :)

I see that you have had your question answered, but can you think of an isomorphism between any two groups of order p where p is prime? I think if you do this, you might understand it even more.
 

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