I want to know the answer to the following question:
What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?
All the background I'm provided with is that "Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows.". Is that enough to answer the question?
Answer: no