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Mar2-12, 02:02 PM
Sci Advisor
P: 906
there are a couple of "easier" cases you might want to look into first:

|G| = pq, p,q distinct primes.

|G| = pk, p a prime.

the second case is "harder", although you may have proved both of these already if you have covered the sylow theorems.

by the way, any group of prime order is necessarily cyclic (why?).