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WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
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 Field: Algebra

Why do we have this article and Group (mathematics)? I think this article should be deleted. Wilmot1 15:38, 18 October 2007 (UTC)

This article, like simple group or CA group, describes a certain type of Group. The "A" in "A group" is an abbreviation for abelian, similar to "Z-group" a group whose sylow subgroups are Zyclic or ztudied by Zassenhaus. JackSchmidt 16:32, 18 October 2007 (UTC)

In which case it should be re-named 'Abelian Group' it's current name is misleading - now I understand what it is about I will be able to contribute, I specialised in Abstract Algebra in my Mathematics BSc. I had never seen the abbreviation 'A' used for abelian. Wilmot1 13:57, 19 October 2007 (UTC)
But also why have we got Abelian group as a separate page? Wilmot1 14:02, 19 October 2007 (UTC)

Merger proposal[edit]

Since the 'A' stands for 'Abelian' I am proposing that this page be merged with Abelian group Wilmot1 14:09, 19 October 2007 (UTC)

An A-group need not be abelian. The two concepts are completely different. It would be wholly inappropriate to merge the articles. JackSchmidt 17:52, 19 October 2007 (UTC)

Expanding on JackSchmidt's comment a bit, the "A" in "A group" is an abbreviation for "abelian". This does not mean that "A group" is an abbreviation for "abelian group". As stated in the article, a group is an A group if its Sylow subgroups are abelian. The smallest nonabelian example is Sym(3), the symmetric group on three points. The order of this group is squarefree (6 = 2•3), so its Sylow subgroups are abelian, implying that Sym(3) is an A group. I oppose this merge. Michael Slone (talk) 04:18, 20 October 2007 (UTC)

Agreed. The proposal to merge is based on a misunderstanding that A-group is synonymous with abelian group. But notice that there is nothing in the current article to dispel that misunderstanding! Putting the example of Sym(3) into the article would help a lot.

BTW, I think the terminology is almost comically bad, but I suppose it appears in the original literature and is not being promoted here, so there is little that can be done about it. Except: how about "A-group" instead of "A group"; this forestalls a who's-on- first routine along the lines of "A group is..." 08:20, 22 October 2007 (UTC)Plclark

In case anyone does feel led to change this article to "A-group", be aware that there is already A-group, which is a redirect to the archaeological article A-Group, so a dab page would probably be useful. Michael Slone (talk) 12:30, 22 October 2007 (UTC)
But I don't think that A-group should redirect to A-Group. The current redirect is only there as a result of that article having been given the wrong capitalization to start with. So I think we should have the mathematical article at A-group and the archeological article at A-Group, with the usual "for the ... meaning, see ..." type of line at the beginning of each. --Zundark 10:39, 25 October 2007 (UTC)

Requested move[edit]

The article title should be hyphenated. --Zundark 14:35, 30 November 2007 (UTC)

I agree. Also whoever is moving should make sure to "have the mathematical article at A-group and the archeological article at A-Group, with the usual "for the ... meaning, see ..." type of line at the beginning of each." JackSchmidt 16:01, 30 November 2007 (UTC)
The only page linking directly to A-group (lowercase) is a draft/old section of Sahara on Talk:Sahara#Nubians so the move shouldn't cause much trouble. JackSchmidt 16:09, 30 November 2007 (UTC)
This seriously needs dabbing. 22:39, 3 December 2007 (UTC)
Based on the above and the naming conventions, I suggest
A groupA-group (group theory)
A-GroupA-Group (people) or (culture) or (Nubians)
A group and variations redirect to A-group, which becomes a disambiguation page to disambiguate between the two
Pomte 08:44, 16 December 2007 (UTC)
But the naming convention that you link to suggests we should put the articles at A-group and A-Group, with disambiguation links at the top of the pages. The more complicated scheme that you're suggesting doesn't seem to have any advantage over this, and just makes linking more tedious. --Zundark (talk) 09:13, 16 December 2007 (UTC)
You're right, I've somehow misinterpreted what I read yesterday. In this case I support the move to A-group. –Pomte 04:01, 17 December 2007 (UTC)

Fact checking, citation finding[edit]

Section 9 of Hall's 1940 "The construction of soluble groups" appears to be a gold-mine of information on soluble A-groups, but it has no proofs and is very, very brief. Is anyone interested in (a) checking whether the statements are correct, (b) checking whether they remain true for insoluble A-groups, (c) finding citations for the material? A summary of the work in the soluble area is available in Huppert's Endliche Gruppen. I haven't checked Doerk-Hawkes yet. JackSchmidt (talk) 20:00, 12 February 2008 (UTC)