The torsion generating set of the mapping class groups and the Dehn twist subgroups of non-orientable surfaces of odd genus

Abstract

A bstract . Let N g be the non-orientable surface of genus g , MCG ð N g Þ the mapping class group of N g , T ð N g Þ the index 2 subgroup generated by all Dehn twists of MCG ð N g Þ . We prove that for odd genus, (1) if g ¼ 4 k þ 3 ð k b 1 Þ , MCG ð N g Þ can be generated by three elements of finite order; (2) if g ¼ 4 k þ 1 ð k b 2 Þ , T ð N g Þ can be generated by three elements of finite order.