uncool Posted November 12, 2006 Share Posted November 12, 2006 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- Link to comment Share on other sites More sharing options...
daniel_haxby Posted January 29, 2007 Share Posted January 29, 2007 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 Link to comment Share on other sites More sharing options...
Dave Posted January 29, 2007 Share Posted January 29, 2007 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. Link to comment Share on other sites More sharing options...
uncool Posted February 11, 2007 Author Share Posted February 11, 2007 Ooo, that looks like a nice proof...will take me a little while to understand it, as I don't know the Sylow theorems... Link to comment Share on other sites More sharing options...
matt grime Posted March 7, 2007 Share Posted March 7, 2007 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. Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted March 7, 2007 Share Posted March 7, 2007 We're not going to improve if our members have that attitude. Stay on topic, please. Link to comment Share on other sites More sharing options...
hotcommodity Posted March 7, 2007 Share Posted March 7, 2007 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 Link to comment Share on other sites More sharing options...
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