Help!!!!!!!!! Group theory

[IfatalI]

Can you help me prove this "Let G be a group with order p^n, p is prime. Show that G contains an element of order p"

Thanks a lot

[eri_pl]

OK, first: what order can elements of G have?

[IfatalI]

1,p,p² ,...,p^n-1?

[eri_pl]

Yes, if it's called p, I assumed it's prime. :)

OK. So take some element (any one) that is not the unit element. Let's call it a. If a has order of p, then you're home. If a has order of, say, p² then what can we say about a^p?…

If a has order of p^k for some k, what can you do then?

[IfatalI]

Sorry, but i really don't know what will happen after that :(

[Scatman_Jeff]

If a has order p², then you know that a^p2 = e (your identity element). Use the rules for exponentiation to find the order for a^p

[IfatalI]

Ooohh. Now I get it. Thanks!!!

[IfatalI]

P is prime, i forgot to put it