Generating the Mapping Class Group by Two Torsion Elements

Abstract

We prove that the mapping class group of a closed connected orientable surface of genus \(g\ge 6\) is generated by two elements of order g. Moreover, for \(g\ge 7\), we obtain a generating set of two elements, of order g and \(g'\), where \(g'\) is the least divisor of g greater than 2. We also prove that the mapping class group is generated by two elements of order \(g/\gcd (g,k)\) for \(g\ge 3k^2+4k+1\) and any positive integer k.