Talk:Cayley table

message: The sentence:
"The Cayley table tells us whether a group is abelian. Because if the group operation of an abelian group is commutative, the Cayley table of an abelian group is symmetric along its diagonal axis."
does not seem totally clear, for two reasons: first, every abelian group is commutative (so the condition "the group operation of an abelian group is commutative" is always fulfilled) and second it could (should?) be stated as an equivalence : 
"The Cayley table tells us whether a group is abelian or not: the group operation is commutative if and only if the Cayley table of the group is symmetric along its diagonal axis."
Don't you think so?
164.81.50.98 (talk) 09:00, 22 September 2009 (UTC)
thread_title: Clarification of Commutativity subsection

message: Perhaps someone should add a simple example to this page like
    + 0 1
    0 0 1
    1 1 0
I might do it later but in the meantime, back to work .... OoberMick 11:04, 9 Jun 2005 (UTC)
thread_title: Request for simple example

message: I created a Cayley Table generator and identifier applet, but I do not know if it is appropriate to add an external link to it.  Jhbarr 16:46, 18 October 2007 (UTC)
thread_title:  Caryler table applet 

message: I don't understand the reasoning at the end of the article's long example: "As we have managed to fill in the whole table without obtaining a contradiction, we have found a group of order 6".  I agree that the structure obtained is a group of order 6, but I don't enough work has been done in the example to deduce that it's a group, because associativity was not checked.  Or did I miss something?  —Preceding unsigned comment added by 134.193.88.39 (talk) 15:56, 11 May 2008 (UTC)
replies: text: I agree.  It does not appear to me that enough conditions have been checked.  A very similar argument in structure is coset enumeration, and there if a "cayley" table is filled in (at least the columns corresponding to generators, and the rows corresponding to coset representatives of a subgroup H), then the order of the group (or at least the index of H in G), is found.  Using H=1, this does allow you to fill in a few columns of the Cayley table from a presentation of the group. JackSchmidt (talk) 16:09, 11 May 2008 (UTC)
replies: text: I guess the question then is, is it possible to follow this algorithm and obtain a Cayley table for a quasigroup that is not also a group?  Most of the algebraic manipulations used here require associativity, but it's true that an exhaustive check has not been performed.  It's an interesting question... 72.42.181.162 (talk) 17:05, 13 July 2008 (UTC)
thread_title:  Cayley table reasoning 

message: I dont follow the reasonning in the grid where 'e' is marked in d*f box instead of d* d box etc. I mean if e is the identity element ? Hexagone59 (talk) 20:50, 25 December 2015 (UTC)
thread_title: paragraph Filling in the identity skeleton

message: I think there is an error in the example table. The text states "a is its own inverse, b and c are inverses, and d and f are inverses." but the table later on indicates, that b and c are its own inverses as well.  — Preceding unsigned comment added by Jakubt (talk • contribs) 14:05, 24 September 2018 (UTC)
thread_title:  Error in table