The generation of \(\text{Sp}(\mathbb F_2)\) by transvections
The symplectic groups \(\text{Sp}_{2n}(F)\) are generated by their transvections, and the minimal number of factors, \(t\), required to express a given \(\sigma\) in \(\text{Sp}_{2n}(F)\) as a product of (symplectic) transvections satisfies \(\text{res}\,\sigma\leq t\leq \text{res}\,\sigma +1.\) Here we determine the elements of \(\text{Sp}_{2n}(\mathbb F_2)\) for which \(t=\text{res}\,\sigma +1\), filling a gap in \textit{J. Dieudonné} [Summa Bras. Math. 3, 149--178 (1955; Zbl 0067.01201)].
minimal number of factors of elements expressible as product of symplectic transvections
scientific article; zbMATH DE number 3537933