Generating the Extended Mapping Class Group by Three Involutions

We prove that the extended mapping class group, $\mathrm{M}\mathrm{o}{\mathrm{d}}^{\ast }({\mathrm{\Sigma }}_{\mathrm{g}})$, of a connected orientable surface of genus $g$, can be generated by three involutions for $g\ge 5$. In the presence of punctures, we prove that $\rm Mod^{*}(\Sigma_{g,p})$canbegeneratedbythreeinvolutionsfor$g\geq 10$and$p\geq 6$(withtheexceptionthatfor$g\geq 11$,$p$shouldbeatleast$15$).