Algebraic subgroup

An algebraic subgroup of an algebraic group is a Zariski topology 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 algebraic variety.

This may also be generalized by allowing scheme (mathematics) 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 .