ON THE MARGULIS CONSTANT FOR

KLEINIAN GROUPS, I CURVATURE

F. W. Gehring G. J. Martin

Abstract. 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 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 ⟨f, g⟩ is nonelementary and discrete with f parabolic or elliptic of order n ≥ 3, then every point x in H^{3} is moved at least distance c by f or g where c = .1829 . . .. This bound is sharp.

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