Transvection conjugacy over a finite field
= Transvection conjugacy over a finite field
Every nonidentity <transvection> has an adapted basis in which it is $I+E_{12}$. Thus all such maps are conjugate in the <general linear group>. In dimension at least three, a scaling of a third basis vector centralizes this matrix and has arbitrary nonzero determinant; adjusting a conjugator by this scaling proves conjugacy in the <special linear group> as well.
// Target: algebra.bigb