Talk:Extension problem

From Wikipedia, the free encyclopedia

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)

[edit] 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)

[edit] Mistake

The claim that Ext¹(H,K) classifies central extensions of H by K is wrong. Ext¹ classifies only abelian extensions. Central extensions are classified by group cohomology, namely H²(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)