# Changes

Let $H$ be the subgroup of $G$ generated by the automorphisms: $e_i \mapsto e_i + re_j, r \in F, i < j \le 0$ and: $e_i \mapsto e_i + re_j, r \in F, 0 < i < j$ Basically, we have partitioned the set $\mathbb{{fillin}Q}$ into two totally ordered subsets: the non-positive and the positive numbers, and are only considering the automorphisms in $G$ that keep each part within itself. For an automorphism of the vector space to preserve $H$, it must either preserve both parts of the partition, or interchange them. However, since $G$ is unitriangular, it cannot send anything in the positive part to anything in the non-positive part. Therefore, it cannot interchange the parts, and therefore it must preserve both parts. We can then show that this forces the normalizing element to be within $H$.