Borel subgroup is abnormal in general linear group

Statement
Let $$k$$ be a field, and $$GL_n(k)$$ denote the fact about::general linear group: the group of invertible $$n \times n$$ matrices over $$k$$. Let $$B_n(k)$$ denote the Borel subgroup of $$Gl_n(k)$$: the subgroup of invertible upper-triangular matrices. Then, $$B_n(k)$$ is an fact about::abnormal subgroup inside $$GL_n(k)$$.

For finite fields
Suppose $$k$$ is a finite field of order $$q$$, where $$q$$ is the power of a prime $$p$$. Then, the Borel subgroup $$B_n(k)$$ is the normalizer of a $$p$$-Sylow subgroup of $$GL_n(k)$$: the subgroup of upper-triangular matrices with $$1$$s on the diagonal. The abnormality in this case follows from the general fact that the normalizer of a Sylow subgroup is abnormal.