Talk:Stable group

The article should probably be renamed to "groups of finite Morley rank" or the "Cherlin-Zilber conjecture" since those are the subjects discussed. Stable groups are considerably more general. For example, the additive group of integers (Z,+) is stable but abelian groups of finite Morley rank decompose as D*C where D is divisible and C has bounded exponent. Indeed, free groups are stable while :
 * 1) groups of finite Morley rank have finite composition series
 * 2) an interesting non-algebraic nilpotent group of finite Morley rank was a highly non-trivial construction of Baudisch.
 * 3) an interesting non-algebraic solvable but not nilpotent group was only achieved two years ago by Wagner, Baudisch, etc.  —Preceding unsigned comment added by 204.52.215.123 (talk) 17:47, 21 November 2008 (UTC)


 * While the smaller class of groups of finite Morley rank is of course the more important one, this may well change as a result of Sela's work on free groups. Anyway there is a lot to be said about stable (and simple) groups in general, so that if we rename this article, an article with the current name will be created sooner or later. It's probably best to split the article once there is so much information on one (or both) of the topics that this is actually required. Of course, if you would like to extend the material on groups of finite Morley rank, go ahead.
 * If you want to do this specifically under Group of finite Morley rank (splitting the article, which is OK, though I wouldn't do it) you can do this as follows: Go to the article. It will redirect to the present article, but with a little note "(Redirected from Group of finite Morley rank)" at the top. If you click the link in this note you are taken to the redirect page. By editing it like any normal article you can remove the redirect and start a new article. --Hans Adler (talk) 20:22, 21 November 2008 (UTC)