 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 126, Number 3, March 1998, Pages 877880
S 00029939(98)04458X
SIMPLE QUOTIENTS OF HYPERBOLIC 3MANIFOLD GROUPS
D. D. LONG AND A. W. REID
(Communicated by James West)
Abstract. We show that hyperbolic 3manifolds have residually simple fun
damental group.
1. Introduction
Let G be a finitely generated group and X a property of groups, e.g. finite,
simple, pgroup. G is said to be residually X, if for any element g = 1, there is a
group H with property X and a surjective homomorphism : G H such that
(g) = 1.
Of interest to us are residual properties of groups 1(M) where M is a compact
orientable 3manifold with infinite fundamental group. Now it is wellknown that
if M is a hyperbolic 3manifold, that is the quotient of hyperbolic 3space by a
torsionfree Kleinian group, then 1(M) is residually finite. In this note we prove
a much stronger result which seems to have been unnoticed previously. First we
make a definition.
