Talk:Composition series

I don't see it as a good idea to merge this with solvable groups. For example where the simple group page links here, the point would surely be lost.

Charles Matthews 15:39, 21 Aug 2003 (UTC)

modules
Could someone add a section on composition series of modules?

I have now done this. I removed some earlier text, because it was not clear (to me, at least), whether the author meant to be dealing with a composition series for the regular module of a finite-dimensional algebra, or was thinking of something elseMessagetolove 02:10, 7 May 2007 (UTC)

Have included some introduction/motivation. Messagetolove 16:43, 21 May 2007 (UTC)

I am not sure what the previous editor had in mind, and I have reverted the previous edit: for example, a field K is certainly an Artinian ring, but there are infinite dimensional vector spaces over K, and these are NOT finitely generated K-modules.Messagetolove (talk) 12:30, 20 April 2010 (UTC)

FTA via JH
I have not reverted the anonymous edit of June 1, 2007, as I agree more or less that JH is a much more complex result than FTA, and I had left this example in out of respect for a previous editor's efforts. But logically, I do not see that JH for finite groups needs FTA. JH for finite groups only really needs that fact that if M,N are different maximal normal subgroups of a finite group G, then MN = G, which needs no arithmetical argument. Also, the fact that a simple finite cyclic group has prime order does not need FTA.

If H is cyclic of order n = ab, a, b integers both greater than 1, then H has (normal) subgroups of order a and b, so is not simple. Messagetolove 00:50, 2 June 2007 (UTC)


 * You should have reverted it because it's wrong, as you pointed out. This is a standard application and indeed unique factorization is proven in this Jordan-Holder manner in more general situations.  So the anon's deletion really needs to be justified.  Some books that note this fact are Rotman and John Roses' books on group theory (which I found through Google books).  The more general applications are in more advanced book.  --C S (talk) 05:32, 6 November 2008 (UTC)

Other languages
The german definition is included here: http://de.wikipedia.org/wiki/Reihe_%28Gruppentheorie%29#Definitionen please add it to the 'other-language-list' (I dont know how to...)

Etymology of "composition factor"
In the article, the term "composition factor" is defined. I think, this immediately raises the question, why it is called "factor". It seems "factor" shouldn't be taken too seriously, because composition factors are not the factors in some kind of product operation. So it would be nice if someone can say something on the history of the terminology, why it is called "factor". Zaunlen (talk) 22:39, 12 November 2019 (UTC)