Algebraic subgroup

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An algebraic subgroup of an algebraic group is a Zariski closed subgroup. Generally these are taken to be connected (or irreducible as a variety) as well.

Another way of expressing the condition is as a subgroup which is also a subvariety.

This may also be generalized by allowing schemes in place of varieties. The main effect of this in practice, apart from allowing subgroups in which the connected component is of finite index > 1, is to admit non-reduced schemes, in characteristic p.

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