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

作者：Du, Xiaoming^*

来源：Hiroshima Mathematical Journal, 2020, 50(2): 199-206.

• mapping class group
• non-orientable surface
• generator
• torsion

Let N-g be the non-orientable surface of genus g, MCG(N-g) the mapping class group of N-g, J (N-g) the index 2 subgroup generated by all Dehn twists of MCG(N-g). We prove that for odd genus, (1) if g = 4k + 3 (k >= 1), MCG(N-g) can be generated by three elements of finite order; (2) if g = 4k + 1 (k >= 2), J (N-g) can be generated by three elements of finite order.