Talk:Coset

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Systems of common left/right coset representatives

See the discussion in Talk:four color theorem.

coset space

Need a discussion of the notation G/H (even in the non-normal case) and similarly for H\G. Dmharvey 20:07, 18 April 2006 (UTC)[reply]

This notation is not completely standard and you don't find it in most introductory modern algebra texts. I am not in favour of introducing additional notation unless it is needed and assists with the exposition. In this case I just don't see the need. It isn't as if we are going to have to repeatedly refer to the set of cosets and hence need a space saving notation for it. For an encyclopedia entry I think it makes sense to try to keep notation to a minimum. Hence I vote no Hawthorn 05:17, 30 May 2007 (UTC)[reply]

Umm, isn't it standard among anyone who would use H\G or more than one action? Well, it does need to be discussed, if only to list which areas use it which way. Wikipedia isn't a text book with it's own consistant notation. Instead Wikipedia does need to concisely explain all common notations. The point is that researchers in other areas and graduate students come here to figure out what is going on with the basics in other articles that they are reading. 134.157.19.52 (talk) 10:57, 7 April 2008 (UTC)[reply]

picture

I have a picture that illustrates coset, among other things, let me know how I can tweak it so it fits with the terminology of the current article--Cronholm144 09:34, 31 May 2007 (UTC)[reply]

I agree. Some pictures would be helpful

--Farleyknight (talk) 07:13, 22 February 2009 (UTC)[reply]

Coset multiplication

I can also draw an image for coset multiplication, but the article barely mentions it in the quotient groups sub section. Let me know if you want the image--Cronholm144 10:09, 31 May 2007 (UTC)[reply]

In the introduction I don't get a general Idea of what a coset is. So it is actually difficult for me, reading through the article, to understand what a coset.

Unfriendly?

For someone coming in cold, this is probably confusing. If they have recently come to understand sets and groups, the notation gH could be obscure; and

{gh : h an element of H }

more so. An educated guess would be that gH means "apply the group operation in turn to g and every member of H", yielding a subgroup of G as the result so that, if the members of H are h¹, h², h³, etc, the coset is gh¹, gh², gh³, etc.

If I've got this correct (can anyone confirm?), a textual description preceding the more formal exposition would be helpful. Fishiface (talk) 18:50, 5 November 2008 (UTC)[reply]

That's almost right. But gH isn't a subgroup unless

g\in H

, in which case gH = H. To see why that's the case, note that the cosets partition the group into (disjoint) subsets and the identity belongs to H. Can you think of a better way to phrase what's there? I'm coming at it from having already studied this, so it's hard to spot unclear bits. Rswarbrick (talk) 18:04, 23 December 2008 (UTC)[reply]

Example

All examples currently are of cosets in an abelian group. Abelian groups are atypical and use the alternative additive notation. I think the first example should be typical and use the more common multiplicative notation. How about using $\ \langle (12)\rangle \leq S_{3}\$ as the first example instead.