#13||Group of prime order is Cyclic ||Maths for Graduates

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  1. Maths For Graduates
  2. group of prime order is Cyclic
  3. if order of group is prime then it is cyclic
  4. cyclic group
  5. group of order prime is cyclic
  6. o(G)=p then G is cyclic
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Couple of notes..
1. How can one just assume that there exists an element "a" which has a order n?
2. Moreover, how can there be a subgroup H other than G and e if order of G is prime?
.
Combining 1 and 2, it's like just assuming that G is cyclic (with a different name H) containing a generator "a" and then just showing the same thing again. My point being that it was never shown that there will absolutely always be an element "a" within G such that a^n=e. You show that and you have your proof. Merely assuming it is not the proof.
.
Edit: Ignore coz there's a proof that in a finite group, all elements have an order. So your proof is correct but it needs to mention this necessity.

kishanprakash