Free actions of finite Abelian groups on the 3-torus (Q1313944)

The authors classify free actions of finite Abelian groups on a 3- dimensional torus. For a finite group \(G\) acting freely on a 3-torus \(T\), \(\Gamma= \pi_ 1 (T/G)\) is a Bieberbach group. First, they list up all the 3-dimensional affine Bieberbach groups, and for each group \(A\) in the list, they give a complete list of all free actions (up to topological conjugacy) of Abelian groups \(G\) on \(T\) which yield an orbit manifold homeomorphic to \(R^ 3/A\).