Generating the mapping class group by two torsion elements (Q2113565)

Let \(\Sigma_g\) be the closed, orientable connected surface of genus \(g\) and \(\mathrm{Mod}(\Sigma_g)\) the corresponding mapping class group. Theorem 1. \(\mathrm{Mod}(\Sigma_g)\) is generated by two elements of order \(g\) for \(g \ge 6\). Theorem 2. For \(g \ge 7\), \(\mathrm{Mod}(\Sigma_g)\) is generated by two elements of order \(g\) and order \(g'\) where \(g'\) is the least divisor of \(g\) such that \(g'>2\). Theorem 3. For \(g \ge 3k^2 + 4k + 1\) and any positive integer \(k\), the group \(\mathrm{Mod}(\Sigma_g)\) is generated by two elements of order \(g/ \gcd(g, k)\).