Talk:Commutator subgroup

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I changed f(G') being a subset of H' by subgroup (since G' is a subgroup, not just the set of generators (it's the generated ("spanned") subgroup)) and thus f(G') is a subgroup of H. But f(G') is contained in the subgroup H', and thus taking the intersection H' \cap f(G') gives the subgroup f(G') drini ☎ 05:31, 31 May 2005 (UTC)

[edit] Title

Why is this "derived group" and not "derived subgroup"? Dysprosia 09:10, 13 February 2006 (UTC)

I think it would be better to call the article derived subgroup (or commutator subgroup). I also question the notation G¹. I don't think I've ever seen this notation before - usually G' or [G,G] is used, or sometimes (in the context of the derived series) G⁽¹⁾. --Zundark 12:54, 14 February 2006 (UTC)

I agree with you (derived subgroup should be fine, I think that is more common, but I haven't done a Google-check). Dysprosia 07:10, 15 February 2006 (UTC)

I've just tried Google (Web, Groups and Books), and also Zentralblatt. All four of these searches indicate that "commutator subgroup" is more significantly more common than "derived subgroup". (Some of these seaches get more hits for "derived group" than for "derived subgroup", but this could be due to the non-mathematical usages. I don't think there is any non-mathematical use of the expression "commutator subgroup".) So I suggest we move the article to commutator subgroup. --Zundark 08:49, 15 February 2006 (UTC)

Sounds fine, then. Go for it. Dysprosia 11:59, 15 February 2006 (UTC)

OK, I've moved the article to commutator subgroup. --Zundark 12:47, 15 February 2006 (UTC)

[edit] Notation

As pointed out above, the notation G¹ is unusual. If there are no objections, I intend to change it to [G,G] (because the alternative G' is too easily misread as G in some fonts). --Zundark 12:49, 15 February 2006 (UTC)

The notation G⁽ⁿ⁾ is nice in some respects because the condition for a group to be solvable is that there exists some n such that G⁽ⁿ⁾ = {e}, echoing ideas of differentiation somehow. But you are right, it isn't all that common. I much prefer G', but [G, G] should be okay too, though it might look a bit cumbersome in the article.