Generating Extended Mapping Class Groups with Two Periodic Elements

The extended mapping class group of a surface $\mathrm{\Sigma }$ is defined to be the group of isotopy classes of (not necessarily orientation-preserving) homeomorphisms of $\mathrm{\Sigma }$. We are able to show that the extended mapping class group of an $n$-punctured sphere is generated by two elements of finite order exactly when $n≠4$. We use this result to prove that the extended mapping class group of a genus 2 surface is generated by two elements of finite order.