# Quasi-split group

quasi-splittable group, over a field $k$

An affine algebraic group (cf. Affine group; Algebraic group) defined over $k$ containing a Borel subgroup defined over the same field. Every affine algebraic group becomes a quasi-split group for some extension of the ground field, for example, over the algebraic closure of this field. Every affine algebraic group defined over a finite field $k$ is quasi-split over $k$. See also Split group.

A group can be quasi-split over $k$, or $k$-quasi-split, without being $k$-split.