Split algebraic group

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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.