Group whose order is product of 2 primes

Asked Mar 14 '17 at 12:56

Active Mar 14 '17 at 13:04

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How it is true that a group whose order is the product of two primes is a cyclic group?

Consider a group of order $6=2\times 3$. I know $O(\mathscr{S}_3)=6$ but $\mathscr{S}_3$ is not cyclic.

Is there some additional info about the result stated above?

Kindly provide the proof for it too.

edited Mar 14 '17 at 13:04

Shaun

asked Mar 14 '17 at 12:56

user424589

3

The group is guaranteed to be cyclic if the group order is $pq$ , $p<q$ and $p$ does not divide $q-1$ – Peter Mar 14 '17 at 12:59
Ohh,any proof of this result? – user424589 Mar 14 '17 at 13:02
Google Sylow's theorem. This is the key to prove this and similar results. – Peter Mar 14 '17 at 13:03
Please share your thoughts so far :) – Shaun Mar 14 '17 at 13:05

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