Talk:Klein four-group

message: I hate this not-working links... I'm not a mathematician but isn't a Cayley table
essentially a multiplication table? Can't we just say
Its Cayley table is given by:
plz? ;) — Preceding unsigned comment added by 82.82.137.56 (talk • contribs) 
:I am a mathematician (though in a different subfield), and I second this.  Similarly, I'd much prefer use of the term direct product rather than a direct sum, since the former has a much clearer definition for my students (like a Cartesian product), while a direct sum is only known by graduate students. Also, here's an example figure with right symmetry group.
 — Preceding unsigned comment added by 68.232.123.66 (talk • contribs) 
Since I don't usually contribute diagrams to Wikipedia, I can't complain much, but I think the lead figure would be a little more helpful if it illustrated the actual 4 symmetries/positions of a rhomb/rectangle with labels on its vertices. 86.127.138.67 (talk) 21:45, 15 April 2015 (UTC)
thread_title:  multiplication table / lead figure 

message: The Klein four-group is not the automorphism group of any simple graph (this is apparently a basic theorem). A credible proof is given on PlanetMath. The graph in this article was simple (having at most one edge joining each pair of nodes), and therefore wrong. I have removed it.
: This was reverted with a correction EmmetCaulfield 13:35, 21 October 2007 (UTC)
thread_title:  Solution 

message: I think there's a problem with this article, and at least some of the other ones on the dihedral and symmetric groups, in that the emphasis seems to be on abstruse demonstrations of the cleverness of the "owners" of the article rather than on the explanatory or illustrative power of an explanation. The "simple graph" here is a case in point: it may well be true that V4 is the automorphism group of the given graph with the given labeling of the vertices. Quite honestly, at my beginner's level of knowledge, it's very hard to tell without a great deal of mental gymnastics, and it seems clear from the above comments that I am not alone. What is certainly true is that V4 is not the automorphism group of any graph with the usual simple vertex labeling, but is the automorphism group of a doubly-connected two-node graph with this usual labeling, and that these facts have substantial explanatory value, since the automorphisms can be applied mentally to the graph without having to simultaneously juggle the labeling of vertices. Can we not teach the triple somersault first, and work in the back-flips later?
In a similar way, the article on D3/D6 (depending on your notation) explains it in terms of permutations. This is more of an explanation of S3, though, isn't it? Now, I know that the two are isomorphic, but surely it would be of much greater pedagogic value to explain D3 purely in terms of reflections and rotations, as the dihedral groups are defined, and then proceed to point out the isomorphism with S3, defined in terms of permutations? As it stands, the isomorphism is tacitly assumed, and the geometric interpretation is entirely ignored. But, precisely because of this isomorphism, the only "difference" is one of the semantics of the interpretation: if you interpret the group as permutations, you have S3, if you interpret it as reflection and rotation, you have D3. That these two are, or should be, the same, is not obvious unless you have substantial expertise, and those with this expertise are not the target audience. I am the target audience, and I'm confused.
Quite honestly, and I'm sorry if this sounds harsh, but I think these articles are pretty crummy. They appear to push abstruse cleverness to the front and push clarity to the rear or, worse, exclude it altogether. Apart from being unhelpful and inappropriate to an encyclopædia, it unnecessarily obscures that part of the transcendent beauty, wonder, unity, and intellectual achievement of group theory that would be accessible to people like me if only the explanation was better. That's a damn shame. It does no favours to mathematics. It does, however, make me appreciate the fact that my abstract algebra lecturer is not of the mindset which demands that one should be able to eat the elephant all in one go rather than one bite at a time.
I'm not seeking to attack anyone, I do think it's possible to be so accustomed to something that you honestly don't see how other people find it abstruse and I am often guilty of this myself in other areas. But while I am working on a clearer exposition for consideration here, I'd like the major contributors to this article to consider my comments, as they are intended, in a spirit of good faith and reflect on the expository power of the "up-front", emphasised content of these articles. EmmetCaulfield 13:35, 21 October 2007 (UTC)
replies: text:  Emmet, you are exactly right. This is a common problem with Wikipedia mathematics pages. The aim sometimes appears to be for the editors of the pages to show off their extensive knowledge of the most abstract areas of mathematics, rather than to explain the subject simply and clearly.  —Preceding unsigned comment added by 128.243.220.42 (talk) 11:10, 3 October 2008 (UTC)
thread_title:  Comment 

message: There is a math music group called "The Klein Four Group", is there any article on them?  (btw, I know this might be considered advertisement, but check out "Finite Simple Group (of Order 2)" on Youtube, it's pretty funny).  Peter Stalin 02:22, 2 April 2007 (UTC)
replies: text: We used to have an article on that music group which has rightly been deleted. It is non-encyclopedic (as you appear to have realized yourself). 141.35.26.61 20:57, 3 April 2007 (UTC)
replies: text: Ah, yeah, thought as much...Peter Stalin 03:42, 5 April 2007 (UTC)
replies: text: I'm kind of surprised that the music group doesn't have an entry, actually, given their infamy in the mathematics community - is the discussion pertaining to the deletion still available anywhere? If people are asking for information about a particular topic, I feel like that alone would indicate encyclopedic merit! Frankg 00:26, 10 September 2007 (UTC)

text: Amateur Transplants, a duo of singing medics, have their own page, so why not these guys?--87.194.86.28 (talk) 15:06, 18 November 2007 (UTC)
thread_title:  The music group 

message: Currently the first heading is ==See also==.  RJFJR (talk) 01:47, 1 July 2016 (UTC)
thread_title:  I think this article needs some more headings