Finite Presentation of a Linear-Fractional Group.

In this paper, we show that the coset diagram for the action of a linear-fractional group generated by $u:z\rightarrow \frac{z-1}{z}$ and $v:z\rightarrow \frac{-1}{z+1}$ on the rational projective line is transitive and the coset diagram for the action is connected. Using the coset diagram, we show that $u^{3}=v^{3}=1$ are defining relations for the group. [ABSTRACT FROM AUTHOR]