Talk:Dihedral group of order 6

His article has a number of problems. For example, in the multiplication table we find the elements a, b, c, d, e. but only a and b are mentioned in the text. Unfortunately, being currently only a beginner in Group Theory, I am not capable of helping much.

s3!=d3
symetric group vs. dihedral group — Preceding unsigned comment added by 77.127.130.120 (talk) 16:35, 25 November 2013 (UTC)
 * They are isomorphic, so I'm not sure what you mean. Some1Redirects4You (talk) 12:56, 30 April 2015 (UTC)

still too techincal
This article, being something a newbie would read, is rather too technical by using two flips/transpositions as the generators in the fist part. Most intro books would use a rotation and a flip as generators. The reason why the two-flip approach is problematic is that you need to explain for example why aba=bab but this article does not bother with that, although it rambles about associativity. Also, the 30-point action illustration is rather hard to follow, even with a pen in hand. Some1Redirects4You (talk) 13:06, 30 April 2015 (UTC)

Also the section Dihedral_group_of_order_6 would also be rather hard to follow for a newbie. A lot simpler explanation would be to draw the two Cayley graphs using rotation as one generator an show that in the dihedral group one 3-cycle goes "the other way around". Some1Redirects4You (talk) 13:11, 30 April 2015 (UTC)

Change of name?
Since the dihedral group of order 6 and the third symmetric group are isomorphic, is it appropriate the article is named after only one of them? Perhaps 'Non-abelian group of order 6' would be better, or 'The smallest non-abelian group'. Either of these is a more accurate description, and also goes some way towards explaining why the subject is important. Robodile (talk) 19:09, 18 January 2016 (UTC)

Inconsistency between Cayley tables
The Caley table shown on the right column below the cycle graph https://en.wikipedia.org/wiki/File:Symmetric_group_3;_Cayley_table;_matrices.svg seems to be the transpose of the Cayley table in section Summary of group operations. The latter follows the convention described in the Cayley table article where the entry at row x and column y is xy. For example, the table in section Summary of group operations shows in the second row (a) and third column (b) the value d which corresponds to (123) in cycle notation (or RGB in the notation in the section before), and which is ab where a = (12) or RG and b = (23) or GB and where xy is interpreted as "do y first and x second", consistent with function composition. On the other hand, the Cayley table in the figure shows the element d (i.e. (123)) in the third row and second column (labeled as 4).

There should be consistency between the different notations and conventions used and the article should explicitly state which conventions are being used where. In particular I think the convention should follow the Cayley table article as well as xy representing "do y first and x second" for consistency with other articles.

--Eposse (talk) 17:21, 14 June 2020 (UTC)


 * What you are seeing is a clash of cultures. There was a time when algebraists did not use a notation for the composition of group operations that was consistent with the functional composition notation of calculus (see early editions of Fraleigh's A First Course in Abstract Algebra). After years of fighting this notational battle, they finally caved and started using the "calculus based notation", but only in some situations. General multiplication tables follow the conventions of the Cayley table article and there is no concept of doing something first or second in a multiplication like $xy$.--Bill Cherowitzo (talk) 19:05, 18 June 2020 (UTC)

Why it is called dihedral?
It is important to say what dihedral mean (a two face polyhedral?) A flip interchange faces. Faces are polygons, which can be rotated the number of sides of the polygon. — Preceding unsigned comment added by 2806:106E:B:53E6:F9:F69F:2ED7:3753 (talk) 05:24, 2 September 2022 (UTC)