 
Summary: Topology and its Applications 101 (2000) 143148
Free actions of finite groups on rational homology 3spheres
D. Cooper
, D.D. Long 1
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
Received 1 December 1997; received in revised form 3 June 1998
Abstract
We show that any finite group can act freely on a rational homology 3sphere. © 2000 Elsevier
Science B.V. All rights reserved.
Keywords: Free finite group actions; Rational homology 3sphere
AMS classification: Primary 57M25, Secondary 20E26
1. Introduction
The purpose of this note is to prove the following:
Theorem 1.1. Let G be a finite group. Then there is a rational homology S3 on which G
acts freely.
That any finite group acts freely on some closed 3manifold is easy to arrange: There
are many examples of closed 3manifolds whose fundamental groups surject a free group
of rank two (for example, by taking a connected sum of S1 × S2's) and by passing to a
covering space, one can obtain a manifold whose group surjects a free group of any given
rank. This gives a surjection onto any finite group and hence a free action on the associated
