Products of three word maps on simple algebraic groups (Q1721756)

The main result that the authors obtain is the following Theorem. Let \(\mathcal{G}\) be a simple and simply connected group which is defined and split over an infinite field \(K\) and let \(G = \mathcal{G}(K)\). Further, let \(\tilde {w} : G^{k+l+m} \rightarrow G\) be the corresponding word map. Suppose \(\mathcal{G}\) is not a group of type \(B_2 \) or \(G_2\). Then \(G \backslash Z(G) \subset\operatorname{Im }{\tilde {w}}\). This improves a result of \textit{C. Y. Hui} et al. [Isr. J. Math. 210, 81--100 (2015; Zbl 1343.22006)].