The Torsion Generating Set Of The Dehn Twist Subgroups Of Non-orientable Surfaces

Abstract

Let $N_g$ be the non-orientable surface with genus $g$, $\text{MCG}(N_g)$ be the mapping class group of $N_g$, $\mathcal{T}(N_g)$ be the index 2 subgroup generated by all Dehn twists of $\text{MCG}(N_g)$. We prove that for odd genus, $\mathcal{T}(N_g)$ can be generated by three elements of finite orders.

6 pages, 7 figures