Don't suppose Hil's still lurking?

I'm here, Emily.

Yaaay! Ahem. Last question, I promise. Why is the group of permutations of {1,2,3,...n} non-abelian for n > 2? There doesn't seem to be anything in the chapter to give me an indication of why things are nonabelian -- just tells me that they are. And occasionally that it's lovely that they are (amusing, but not helpful).

(I'm having some musings about rotation composed with reflection being different the other way around, but nothing really concrete.)

To show something's nonabelian, usually the simplest way is just to find two non-commuting elements. So, if n is greater than 2, then you know that, at the very least, it has (12), (13), (23), (123), and (132). If you try out a few combinations of those, you'll probably find a pair that doesn't commute.

But... I'm confused. Those are subsets, but how do they work as permutations?

I am now picturing using meara's boobs as a shelf for something

Sadly, while they are definitely very perky, they are perky because they are not large enough to be used shelfishly.

Admittedly, she saved her best dance for Cybervixen, but I did get a red dress dance with her

Awww. I miss CV. But I do still have the red dress. :)

AWESOME Malyasia pictures, Raquel!! Especially the River Girl one, and the BABY LELEPHANTS!

It explains kids so often hating broccoli and adults losing much of the taste for candy

I'm not supposed to like candy??

All of you talking trash about the ground beef/noodles/cheese/tomatoes options are making me hungry for it. Dang.

Damn Cass, so sorry about the layoff. That sucks a lot.

she's also freaked out cause her SiL messed up dyeing her hair at home and it's purple

I thought you meant B's hair was now purple, and was like "Huh, well, that would be a valid reason to freak out, but it's kinda karma..."

I ate clotted cream and liked it

That's because it's *delicious*

Ack! I got to the end of the thread and it's all mathy!! Eek!

You didn't learn that notation yet? (12) is the permutation that switches 1 and 2 and does nothing to 3. (123) is 1 goes to 2, 2 goes to 3, 3 goes to 1. Etc. Each element goes to the place where the thing to its right was, until you get to the end of the parenthesis and then it cycles back to the beginning. So, in the group of four elements, (12)(34) would switch 1 and 2 and switch 3 and 4.

Ack! I got to the end of the thread and it's all mathy!! Eek!

Yes. The husband type person is watching the Yankees/Angels game. I seek refuge here, only to be mathed at.

Also, my pun got no love, and now I'm worried that it wasn't clear what the "stinks" was in reference to, and that I've offended everyone. It was supposed to be P-C saying it stinks that he missed the swag.

Now I'm all over explainy.

But still? I math not.

Huh. Nope. Or, rather, maybe, but like I said I missed the class. So I get that I can find a noncommuting pair for any particular set, but how do I go about proving the claim for all n > 2?

Tell me if this makes any sense: Dn must be a subset of Sn (right?). Then there's some permutation (reflection or diagonal flip) such that vertex x goes to itself, but all the other vertices change, and also some premutation (rotation) such that all vertices change by 1. Then I can show these don't commute. Would that suffice?

Cindy, I liked the pun.

I'm off to bed. I know--it's ridiculously early. But last night I went to bed early and felt human this morning so I'm going to try for it again tomorrow.