On the Margulis Constant for Kleinian Groups, I
F. W. Gehring and G. J. Martin
The Margulis constant for Kleinian groups is the smallest constant $c$ such that for each discrete group $G$ and each point $x$ in the upper half space ${\bf H}^3$, the group generated by the elements in $G$ which move $x$ less than distance $c$ is elementary. We take a first step towards determining this constant by proving that if $\langle f,g \rangle$ is nonelementary and discrete with $f$ parabolic or elliptic of order $n \geq 3$, then every point $x$ in ${\bf H}^3$ is moved at least distance $c$ by $f$ or $g$ where $c=.1829\ldots$. This bound is sharp.