Talk:Extension problem

I think that the distinction between K being a subgroup of G or only being isomorphic to one is not important, because there is a specific isomorphism between them. This language doesn't really generalize anything, it just makes it a bit more confusing. Gregory Muller 13:58, 11 September 2006 (UTC)

Merge with Group Extension

I'm not sure there are enough interesting things to say about group extensions other than their classification to merit its own entry. Gregory Muller 13:58, 11 September 2006 (UTC)

Well, there are entire articles on group cohomology and the ext functor, so it would seem there's a lot to be said ... linas 20:33, 11 March 2007 (UTC)

Mistake

The claim that $Ext^{1}(H,K)$ classifies central extensions of $H$ by $K$ is wrong. $Ext^{1}$ classifies only abelian extensions. Central extensions are classified by group cohomology, namely $H^{2}(H,K)$, which is a gadget that makes sense after we've specified an action of $H$ on $K$. So, someone should fix this. It may have to be me. John Baez 18:32, 26 January 2007 (UTC)

We'd prefer it was you ... linas 20:35, 11 March 2007 (UTC)

I removed the section. Ext^1(H,K/[K,K]) is zero if K is perfect, so the formula is wrong, but if K is non-abelian then a central extension of K is never abelian, so it does not classify abelian extensions either. JackSchmidt (talk) 15:07, 22 January 2008 (UTC)