The Twıst Subgroup Is Generated By Two Elements

Abstract

We show that the twist subgroup T-g of a nonorientable surface of genus g can be generated by two elements for every odd g >= 21 and even g >= 50. Using these generators, we can also show that T-g can be generated by two or three commutators depending on g modulo 4. Moreover, we show that T-g can be generated by three elements if g >= 8. For this general case, the number of commutator generators is either three or four depending on g modulo 4 again.