Split algebraic group

This article defines a property that can be evaluated for an algebraic group. it is probably not a property that can directly be evaluated, or make sense, for an abstract group|View other properties of algebraic groups

Definition

An algebraic group over a field $K$ (not necessarily algebraically closed) is termed a split algebraic group if it has a Borel subgroup that has a composition series such that all the composition factors (i.e., all the successive group quotients) are isomorphic to either the additive group of $K$ or the multiplicative group of $K$.

Note that if $K$ is an algebraically closed field, then every linear algebraic group (and hence, every affine algebraic group) over $K$ is split.