Let a and b be two simple closed curves on an orientable surface S such that their geometric intersection number is greater than 1. The group generated by corresponding Dehn twists ta and t b is known to be isomorphic to the free group of rank 2. In this paper we extend this result to the case of a nonorientable surface.

Let Ng,s denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski [14] obtained an explicit finite presentation for the mapping class group M(Ng,s) of the surface Ng,s, where s ∈ {0, 1} and g + s > 3. Following this work we obtain a finite presentation for the mapping class group M(Ng,s) with generators being Dehn twists and one crosscap slide. 2000 Mathematics Subject Classification. Primary 57N05; Secondary 20F38, 57M99.

We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups