Abstract Algebra: group G of order 25; prove cyclic or g^5=e

[Jamers328]

Let G be a group of order 25. Prove that G is cyclic or g^5 = e for all g in G.

 

[mmm4444bot]

Re: Abstract Algebra proof



Hello Jamers:

I cannot help with this exercise, but I'm confident that any people who are able to help would appreciate knowing something about what you already know.

Do you have any specific questions about how to handle this exercise? Can you show any work or explain any reasoning?

Also, please read the post titled "Read Before Posting", if you have not already done so.

Cheers,

~ Mark

 

[daon]

Re: Abstract Algebra proof

Assume G is not cyclic and that there exists an element g that is not order 5. What other orders can it be? Can you find a contradiction?

 

[Jamers328]

Sorry about that Mark.

Thank you, daon!