Can a Group of Prime Order Be Proven Cyclic Using Only Basic Group Theory?

kntsy
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How to prove that a group of order prime number is cyclic without using isomorphism/coset?
Can i prove it using basic knowledge about group/subgroup/cyclic(basic)?
I just learned basic and have not yet learned morphism/coset/index.



Can you guys kindly give me some hints or just answer yes/no? No solution for this question please and i am not posting HW.
 
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kntsy said:
How to prove that a group of order prime number is cyclic without using isomorphism/coset?
Can i prove it using basic knowledge about group/subgroup/cyclic(basic)?
I just learned basic and have not yet learned morphism/coset/index.



Can you guys kindly give me some hints or just answer yes/no? No solution for this question please and i am not posting HW.

Are you familiar with Lagrange's theorem? If not, look it up, then take any element of the group and look at the subgroup that it generates. What can you say about it?
 

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