A remark on presentations of certain Chevalley groups.
Let \(\Phi\) be a root system of type \(A_l\), \(l\geq2\); \(D_l\), \(l\geq4\); or \(E_l\), \(6\leq l\leq8\). Let \(G\) be a group generated by nonidentity Abelian subgroups \(A_r\), \(r\in\Phi\), and subject to certain relations that are slightly more general than those given by \textit{F. G. Timmesfeld} [Geom. Dedicata 73, No. 1, 85-117 (1998; Zbl 0919.20021)]. The author shows that \(\Phi\) is the disjoint union of irreducible root subsystems \(\Psi_i\) of \(\Phi\) with certain conditions. As a consequence, \(G\) is a central product of groups \(G_i\) which are related to the \(\Psi_i\).
scientific article; zbMATH DE number 1889268