Talk:Abelian group

Wikipedia articles are fairly consistent in writing "Euclidean", "Newtonian", "Eulerian", "Riemannian" with upper-case first letter. Is there any reason why, instead of "Abelian", mostly "abelian" is being used?
S.

We follow the mathematical usage; "abelian" is much more common than "Abelian". Generally, it is considered to be an honour if you have made it to an adjective and are written in lower-case. AxelBoldt

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A stalwart from our lexicon of maths jokes to get us through lectures: What's purple and commutes? An abelian grape.

So, in the unlikely event that you were wondering, that's why the recent anon made those pecular edits! Pete/Pcb21 (talk) 12:45, 9 Dec 2003 (UTC)

Could be someone who's central heating's out and has to travel on a very cold bus to work? Dysprosia 12:47, 9 Dec 2003 (UTC)

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I don't know the right word, so I'll post my addition on this talk page, so that someone can put the corrected version in the article.

A finite group can easily be checked to be abelian by creating its group table (what's "Gruppentafel" in english?): The group is abelian iff the table is symmetric along the main diagonal. --SirJective 12:10, 19 Dec 2003 (UTC)

Group table, probably. Would you like me to add this, or do you want to go ahead? I have something to add related to your potention addition... Dysprosia 12:14, 19 Dec 2003 (UTC)

I'm a bit unsure about my language being correct. After 8 years of English lessons at school I can read and understand the most, but never was good at writing things myself. So I would prefer you to add my sentence. It irritates me that I cannot find the group table in this wikipedia, nor via google... A search in MathWorld yields the term multiplication table... That seems to be the right term!

You may also want to look at Cayley diagram or cayley table as it applies specifically to groups.

See also Talk:Cantor-Bernstein-Schroeder_theorem for another addition, which hasn't inspired anyone since the end of october. --SirJective 12:41, 19 Dec 2003 (UTC)

For this, as you can see, I've avoided the problem altogether :) Dysprosia 23:45, 19 Dec 2003 (UTC)

Fine, thanks. 217.80.248.173 12:24, 20 Dec 2003 (UTC)

lowercase notation a great honor?

Can someone please explain or justify this rather bizarre sounding remark? -Lethe | Talk 15:50, May 5, 2005 (UTC)

First, you are referring to the very first sentence on this talk page. That could have been made explicit, since I first looked at the page history, then at the article, and only later here. But I found it. :)

I think it means to say that once words become generic and widespread, they usually get to be lowercase. Like "gramophone" which I think used to be "Gramophone". Basically the point is that "abelian" is now the defacto spelling, and not "Abelian", which means this lad, called Abel, is very famous now. :) Oleg Alexandrov 16:58, 5 May 2005 (UTC)

So actually I was referring to the final section of the article where it reads:

"The abelian group is rare in being expressed with a lowercase a, rather than A."

I completely missed what that sentence was saying. I thought that somehow denoting abelian groups with a lowercase letter (i.e. let a be the infinite cyclic group) was supposed to be a great honor to the group. Which was fucked up for a whole bunch of reasons: we don't honor mathematical objects, we honor people; most people write groups with capital letters, or at least no one writes the names of ablelian groups in particular as lowercase.

But now I see that the "a" in question was the first letter of the word "abelian", and everything makes perfect sense. Thanks Oleg. -Lethe | Talk 23:02, May 5, 2005 (UTC)

I was thinking about it, and it always seemed to me that when we write abelian group (or sometimes I'll see, for example, euclidean geometry or something), it's lowercase because the word has become so common, not because we're trying to bestow even greater honor on Abel. True, it is a great honor that one of his mathematical inventions is so important and ubiquitous that we deem it a nonproper word. but the lowercase letter isn't there for the honor, it's there to indicate the commonness of the word. Or at least that's my opinion. -Lethe | Talk 22:51, May 12, 2005 (UTC)

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Every commutative ring gives rise to two abelian groups in the same fashion

Shouldn't it be: "every unital commutative ring"? What if there are no units in a ring? Or is that not possible? Andres 21:45, 8 May 2005 (UTC)

Wikipedia's definition of ring doesn't allow non-unital rings. --Zundark 22:05, 8 May 2005 (UTC)