Talk:Examples of groups

Previously untitled section (titled 31 January 2020)

Under "the set of maps":

"And there is a map i such that i(x)=e where e is the unit element of G. The map i makes all the functions f in M(S,G) such that if=fi=f, or i is the unit element of M(S,G)."

Shouldn't the identity function i(x) = x ???

Take, for example, the group of nonzero rationals under multiplication. Then e is 1. And if we let i(x) = 1, we do not get if = fi = f.

This seems pretty undeniable, but I'm just now taking abstract algebra, so maybe I'm misunderstanding the situation. I don't want to presume to correct whoever wrote this without the consensus of other readers. — Preceding unsigned comment added by 129.81.125.99 (talk) 23:21, 3 November 2006 (UTC). (Signature added by SUM1 (talk) 31 January 2020)

How about including some information from Lattice_of_subgroups? That image below looks really neat. Tony (talk) 21:01, 27 August 2010 (UTC)

Previously untitled section (titled 31 January 2020) (2)

The message: "This article does not cite any sources. ... and removed." Is redundant and ruining the math sections of Wikipedia. Furthermore I argue it is based on a mistaken philosophy that does not apply to mathematics articles. The requirement of sources submits us to a circular process that is not consistent with the philosophy of mathematics --- It is circular. For example, there was a time when no one believed in irrational numbers, were we to always require sources we could never publish a discovery of the irrationals. The argument against what I am saying is that this is just an encyclopedia. I think that it is demeaning to require sources and instead a proof is what should be asked for. If a symbolic convention is in question talk about it here on the talk page! In summary the message been placed excessively above the math articles. Berrtus1 (talk) 04:15, 20 May 2016 (UTC)

Needs expansion, 3 times more groups!

The article is good, however, if someone one to expans by adding more groups examples, it would be awesome. It needs them. — Preceding unsigned comment added by Santropedro (talk • contribs) 12:27, 21 January 2017 (UTC)

The group of translations of the plane

In Examples of groups#The_group_of_translations_of_the_plane:

a ∘ b = "move East for 5 miles"

The distance 5 is correct, but the direction is not exactly East. This has to be fixed. VladimirReshetnikov (talk) 17:41, 21 February 2018 (UTC)

You are quite correct, but how to fix it? Fixing the numbers to make it work will introduce a √2, leaving the numbers and fixing the direction will introduce some nasty looking trig if done correctly, leave the 5 and be vague about the direction? Or should we just scrap this example and come up with another? --Bill Cherowitzo (talk) 19:12, 21 February 2018 (UTC)

Inconsistency between text and diagram?

In the first paragraph of section "The symmetry group of a square: dihedral group of order 8", it states that "We could also flip it horizontally so that its underside become up. Again, after performing this movement, the glass square looks the same, so this is also an element of our set and we call it b. " However the associated diagrams all show action b as flipping along a vertical axis. Many would still call this an "horizontal" flip, but the statement that "so that its underside become (sic) up" is wrong. It should be "so that left and right sides are switched" or something along those lines.

--Eposse (talk) 16:53, 7 June 2020 (UTC)

The statement wasn't really wrong but it did need some clarification. I hope I added enough to make this clear.--Bill Cherowitzo (talk) 18:33, 7 June 2020 (UTC)

There is a further inconsistency - in the Dih4 cycle and Cayley diagrams, the representation of ba³ does not match the blue and yellow diagram. I would think that, e.g., ab would mean "b operates on the identity, then a operates on the result" which means the cycle and Cayley diagrams have it backwards. (Evidently there are two conventions relating to Group action). The article should be consistent. PAR (talk) 05:55, 28 October 2022 (UTC)

Ordering of sections

Due to reorganizing of the article in 2018, the sentence "These groups are our first examples of infinite non-abelian groups" in the section on matrix groups is wrong. Of course this doesn't matter and the sentence could just be removed, but it got me thinking: would it be pedagogically better to put matrix groups before free groups or vice versa? I am leaning towards the former because many beginner students are familiar with matrices, and the standard groups of matrices are quite "concrete", plus they give a good example of subgroups. If you agree with this feel free to re-reorganize the article. Joel Brennan (talk) 23:15, 9 December 2021 (UTC)