Generating the mapping class group of a nonorientable surface by three torsions

Abstract

We prove that the mapping class group $$\mathcal {M}(N_g)$$ of a closed nonorientable surface of genus g different than 4 is generated by three torsion elements. Moreover, for every even integer $$k\ge 12$$ and g of the form $$g=pk+2q(k-1)$$ or $$g=pk+2q(k-1)+1$$ , where p, q are non-negative integers and p is odd, $$\mathcal {M}(N_g)$$ is generated by three conjugate elements of order k. Analogous results are proved for the subgroup of $$\mathcal {M}(N_g)$$ generated by Dehn twists.