On linear groups generated by two long root subgroups

Let $k$ be a field of characteristic $\ne2$, $k\ne GF(3)$; let a field $K$ be an algebraic extension of $k$; and let $n\ge 4$ be a natural number. A long root $k$-subgroup is understood to be a subgroup of $SL_n(K)$ conjugate in $GL_n(K)$ to the group constituted by all matrices of the form $\operatorname{diag}\biggl( \begin{pmatrix} 1&a \\ 0&1 \end{pmatrix}, \begin{pmatrix} 1&a \\ 0&1 \end{pmatrix}, 1_{n-4}\biggr), \quad a\in k$. It is proved that every nonabelian group in $SL_n(K)$ without transvections, generated by two long root $k$-subgroups is isomorphic with the group consisting of all upper unitriangular matrices lying in $SL_3(k)$ or the group $SL_2(L)$ over such a field $L$ that either $k\subseteq L\subseteq K$ or $L$ is a quadratic extension of some field intermediate between $k$ and $K$.