Talk:Algebraic group

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Mathematics rating:	Stub Class	Mid Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. With that many refs the article can have more than one section--Cronholm144 02:56, 14 May 2007 (UTC)

Every algebraic group G contains a linear subgroup H such that G/H is an abelian variety, but the sequence 1 -> H -> G -> G/H -> 1 is in general not split. Hence it is wrong to say that G is a semidirect product of H and G/H. Joerg Winkelmann 11:53, 1 May 2006 (UTC)

[edit] Examples

The text says that each finite group G is also algebraic. I think that needs further explaining: why is that? Why is G even the set of zeros of some polynomials (over which field? The group-algebra?). And why are inversion and multiplication morphismns? —Preceding unsigned comment added by 77.189.130.148 (talk) 16:03, 24 March 2008 (UTC)