Abelian subgroups generated by Dehn twists in homeomorphism group

The subgroup of mapping class group generated by Dehn twists along the set of simple closed pairwise nonhomotopic curves with some conditions is studied. It is proved that this group is isomorphic to a free Abelian group of rank $k$, where $k$ is the number of curves in the set. In the case of an oriented surface, this result is classic.