Unipotent elements in subgroups which contain a split maximal torus (Q1902130)

The author studies unipotent elements in a subgroup of a Chevalley group which is generated by two conjugates of a split maximal torus. The main result is the following theorem: Let \(P\) be a standard parabolic subgroup of a Chevalley group \(G\) over a field \(K\) with \(|K|\geq 7\). If \(G\) is of type \(C_\ell\) and \(\text{char }K=2\), assume that \(K\) is perfect. Let \(U_P\) and \(L_P\) be the unipotent radical and Levi-complement of \(P\) and \(T\) a split maximal torus contained in \(L_P\). Express \(x\in P\) in the form \(x=uy\), where \(u\in U_P\), \(y\in L_P\). Then \(u\in\langle T,xTx^{-1}\rangle\). This paper is an interesting contribution to Seitz's programme of description of subgroups which contain a maximal torus.