 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-4/19f/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Every element of

G L_{2} (F_{q})

is conjugate to exactly one representative of one of these types, with the indicated parameter identifications:

$a I$ , where $a \in F_{q}^{\times}$ ;
$(a 0 1 a)$ , where $a \in F_{q}^{\times}$ ;
$diag (a, b)$ , where $a, b \in F_{q}^{\times}$ , $a \neq = b$ , and $(a, b)$ is unordered;
$(01 - N (λ) Tr (λ))$ , where $λ \in F_{q^{2}} ∖ F_{q}$ is identified with $λ^{q}$ .