User talk:Nbarth/Archive 2008

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1 Whitehead lemma steinberg etc.
2 Higher centers
3 Thai names
4 (Wikibooks Welcome)
5 External links on Canon/Photography articles
6 International Standard Book Number
7 Hello

Whitehead lemma steinberg etc.

You added a bit about the derived subgroup of stable GL. If is not too hard, I would appreciate a systematic statement along the lines of "and it is totally false for GL(n,A) even for amazingly reasonable rings A" (including the integers and even some fields), especially if it could mention how to measure how close to true it is.

BTW there was a question on sci.math about whether stable GL determines the ring (up to ring isomorphism). I think it might not, but I think it might determine it up to Morita equivalence which was all that was really needed. Do you happen to know (or find the question interesting enough to find someone who does)?

Also, I've found irritating uses of Steinberg relations versus actual presentations of SL(n,A) for rings A and I am curious how different they are. Generically topologists have access to entirely too much algebra for my taste; it is so hard to figure out what they are talking about. You seem to have a good feel for it (though perhaps you are actually one of THEM), so I thought you might know a good place to find out about SL(n,A) versus Steinberg. I think I only care about amazingly well behaved rings A, like number rings, their fields of fractions (number fields), their completions (mathfrak{p}-adic integers and fields), and their residue fields (finite fields). Heck I might only care about maximal orders in quadratic fields; it is so hard to tell how general the implicit ideas are.

Oh and in the Steinberg group article, it might be good to litter the text with the word "stable", explaining a time or two that this is only about GL(oo,A) not GL(n,A). I keep thinking you are high when I see things like E(A) is perfect, or that the kernel of St(A)->GL(A) is the center of St(A). In fact that last part seems insane even for the stable GL, but I've come to accept stable things are unlike everything I've ever known. JackSchmidt (talk) 07:08, 2 January 2008 (UTC)

(Responding to talk post)

Thanks for the articles. They've been very helpful. No worries about the random questions.

The GL(A) determining A was phrased in the form "K_n(A) is an invariant of GL(A) for positive n, how about for n=0", so it might still be interesting to you (though I still have no idea where to look). For non-commutative A, M_n(A) does not determine A, but does up to Morita equivalence. For commutative rings, Morita equivalence is just ring isomorphism, so I think it should be fine to add "A commutative" or "up to Morita equivalence". However, Units(R) does not determine R, and so GL_n(R) = GL_n(S) does not even imply that M_n(R)=M_n(S). I could not find any examples where this held for all n, so I am not sure if "stable" magically changes things here like it usually does.

"Isn't $\operatorname{E}_n(A)$ always perfect (for $n\geq 3$ ), due to the 2nd Steinberg relation (this struck you as insane)?"

Perfection seems fine, just the idea that the kernel is the center. The "second center" of a perfect group is equal to the center. Saying that the kernel of St(A) to E(A) is the center of St(A) should imply that the center of E(A) is trivial, which, as far as I know, it is not. If St/Z(St) = E and St is perfect, then Z(E)=Z^2(St)/Z(St)=Z(St)/Z(St)=1. This doesn't seem kosher for A=Z/5Z for instance, where I think E_n=SL_n is perfect, and often has nontrivial center.

Probably my mistake is in thinking Z(E_oo) is nontrivial, since Z(E_n(A)) is repeatedly (in n) trivial. JackSchmidt (talk) 23:39, 6 January 2008 (UTC)

Oh and to be clear, I'm in a rush and mean that "should imply that the center of E(A) is trivial, which, as far as I know, ~~it is not~~" contains a mistake. I bet the center of E(A) is trivial. JackSchmidt (talk) 23:43, 6 January 2008 (UTC)

Higher centers

Also discussed at User_talk:JackSchmidt/Archives/2008/01#UCS_:_Hypercenter_::_LCS_:_.3F.3F

(reply to talk post)

"Higher center" is definitely common in spoken math. I think symbols Z^i or "upper central series" may be more common written, but I don't have sources nearby to check. The section looks nice. I linked to upper central series, but that is just a redirect. I can't decide if every little group theory definition needs its own article. I think User:Zundark is improving the Derived length / Derived series situation for soluble groups, so I've avoided thinking about what to do for central series of nilpotent groups. I like your merge of Gruen's lemma into perfect group. I'm pretty sure he has some more important lemmas that could be added eventually, but until then, that article was going to stay pretty stubby. JackSchmidt (talk) 01:30, 9 January 2008 (UTC)

Today's stuff looks good.

There is one point where your text implicitly assumes the reader knows that English ordinals like first, second, third, etc. are taken to imply set theoretic ordinals, including the infinite ones ("the hypercenter the union of the higher centers"), but it was not clear to me that making this explicit would actually reduce confusion. Those who only count using natural numbers are likely to be dealing with noetherian groups anyways, and those who count using set theoretic ordinals should just take it as given.

Schenkman should be able to confirm properties of hypercentral groups. Locally nilpotent groups are slightly more general than hypercentral groups (if I recall correctly), and share most of the same properties. The maximal subgroup being normal worries me slightly, but probably it will be ok since the problem should only be that maximal subgroups need not exist. Hopefully I'll remember to check tonight. JackSchmidt (talk) 23:44, 15 January 2008 (UTC)

Thai names

On the one hand you say that Thai family names are required to be unique, and then you refer to a survey which shows that only 81% of names are in fact unique. This appears to be contradictory and needs explanation. Intelligent Mr Toad (talk) 02:21, 21 January 2008 (UTC)

(Wikibooks Welcome)

Welcome, Nbarth!

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Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard | ^talk 20:58, 22 January 2008 (UTC)

External links on Canon/Photography articles

User talk:Nebrot#Re: Nbarth

User talk:Thegreenj#You think this is spam.3F

Hay Nbarth, I've noticed you have been making a lot of changes to most of the Canon lens/camera articles. Most edits are good, and are productive, but some are beyond the scope of wikipedia. What I am talking about is the abundance of external links, particularly to lens/camera review sites. External links should only be used, to reference text in the article. Using them otherwise, and in such abundance, can be considered Spamming. Now I thought about going trigger happy on your edits, and deleting the links, but I rather not be so abrupt and cruel. It sucks when you spend so much time editing, only to come back an few days later, and see somebody else made changes/deletion to them, and not understand why. I do NOT think you were intending to spam, so I rather give you the opportunity to understand why they should not be there, and remove the links yourself. This is not so much my view point, but the consensus of most wikipedia editors. Having so many external links, makes wikipedia look less like a encyclopedia, and more like a advertisement. While reviews are helpful for someone looking to buy a lens, wikipedia is not the place people should come to, for links to them. Rather, they should come to wikipedia to learn about them. If they want to buy the lens, camera, whatever... and find reviews, then that is what Google is for. If you want to talk further, reply here please. Thanks. Nebrot (talk) 03:10, 25 February 2008 (UTC)

International Standard Book Number

Hello Nbarth. I noticed your recent observation that group identifiers form a prefix code. This does appear to illuminate one feature of how ISBNs work. I wonder if you know anything about the claimed acronym GIC. The cited source for 'group identifier' at isbn.org does not use the acronym GIC, or use the phrase 'group identifier code.' For instance, see [1]. Since 'GIC' has always puzzled me, and I wondered if it was a misunderstanding, do you know if that abbreviation is attested from somewhere else? Or perhaps it comes from a source that is not specific to ISBNs. The simpler 'group identifier' is the phrase that I am used to seeing. Thanks, EdJohnston (talk) 01:49, 1 March 2008 (UTC)

Hello

Question asked an answered at: Wikipedia:Reference_desk/Archives/Mathematics/2008_March_31#cos.28.CF.80.2F2n.29

See also: User talk:Eliko#Excessive_cross-posting

I've seen your important contributions for the article Recurrence relation. I'm looking for the general (non-iterative) non-trigonometric expression for the exact trigonometric constants of the form: $\begin{align}\cos \frac{\pi}{2^n}\end{align}$ , when n is natural (and is not given in advance). Do you know of any such general (non-iterative) non-trigonometric expression? (note that any exponential-expression-over-the-imaginaries is also excluded since it's trivially equivalent to a real-trigonometric expression).

Let me explain: if we choose n=1 then the term $\begin{align}\cos \frac{\pi}{2^n}\end{align}$ becomes "0", which is a simple (non-trigonometric) constant. If we choose n=2 then the term $\begin{align}\cos \frac{\pi}{2^n}\end{align}$ becomes $\begin{align}\frac{1}{\sqrt{2}}\end{align}$ , which is again a non-trigonometric expression. etc. etc. Generally, for every natural n, the term $\begin{align}\cos \frac{\pi}{2^n}\end{align}$ becomes a non-trigonometric expression. However, when n is not given in advance, then the very expression $\begin{align}\cos \frac{\pi}{2^n}\end{align}$ per se - is a trigonometric expression. I'm looking for the general (non-iterative) non-trigonometric expression equivalent to $\begin{align}\cos \frac{\pi}{2^n}\end{align}$ , when n is not given in advance. If not for the cosine - then for the sine or the tangent or the cotangent.