Groups of squarefree order

[uncool]

Are there any nonabelian groups of squarefree order where none of the primes divides any of the others minus 1? If not, is there a proof of this? I've been trying to do this, but the proof for 2 primes doesn't extend, as I can't find how to prove the group with order of the largest prime is normal.

=Uncool-

[daniel_haxby]

I don't know if noone answered this because they thought it was too easy, or they didn't know the answer. I didn't immediately know the answer, but I gave it a go. Here is a proof I knocked up on LaTeX, because I've only just started to learn it and I'm still feeling quite geeky about it.

 

Anyway, here is a (late) answer to your question.

 

Dan

answer.pdf

[Dave]

Thanks for the proof! My group theory isn't so good and I don't generally have the time to answer these questions in detail, but I hate to leave a thread with no answer at all.

[uncool]

Ooo, that looks like a nice proof...will take me a little while to understand it, as I don't know the Sylow theorems...

[matt grime]

I see the standard of mathematics here hasn't improved. Just look at the groups of order what ever. It is trivial to find counter examples.

[Cap'n Refsmmat]

We're not going to improve if our members have that attitude.

 

Stay on topic, please.

[hotcommodity]

I see the standard of mathematics here hasn't improved. Just look at the groups of order what ever. It is trivial to find counter examples.

 

I'll probably get warned for this but dude, you're an asshole. Confine your posts to physicforums where people take your crap and stay away from here