Herstein's Restrictions

[SaSA :::::]

<p style="text-align: left;">Let G be a group of order pq, where p>q are primes. Prove that if q doesn't divide p-1, then G is cyclic, without using Sylow theorems. (You can only use material developed up to section 2.9 of IN.Herstein.)</p>

[Srijit Mukherjee]

https://math.stackexchange.com/questions/67129/groups-of-order-pq-without-using-sylow-theorems

Go through the second answer.

[SaSA :::::]

Thanks, I saw this, but the problem is that Herstein has not introduced much of these ideas up to this problem. I found something different, it goes like this, center Z of G has order either 1 or pq, if q doesn't divide p-1 it can be shown that a normal subgroup of order p is contained in Z, therefore Z=G, so G is abelian and it has an element of order pq.

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