Page "Group scheme" Paragraph 19

When working over a field, one often can analyze a group scheme by treating it as an extension of group schemes with distinguished properties.

Any group scheme G of finite type is an extension of the connected component of the identity ( i. e., the maximal connected subgroup scheme ) by a constant group scheme.

If G is connected, then it has a unique maximal reduced subscheme G < sub > red </ sub >, which is a smooth group variety that is a normal subgroup of G. The quotient group G < sub > inf </ sub > is the infinitesimal quotient, and is the spectrum of a local Hopf algebra of finite rank.