Kummer Group

A Group of Linear Fractional Transformations which transform the arguments of Kummer solutions to the Hypergeometric Differential Equation into each other. Define

$$\begin{eqnarray*} A(z) &=& 1-z\\ B(z) &=& 1/z, \end{eqnarray*}$$

then the elements of the group are $\{I$, $A$, $B$, $AB$, $BA$, $ABA=BAB\}$.