Free actions of elementary abelian groups on tori.
by
Karel Dekimpe
K.U.Leuven Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium
Coauthors: Penninckx Pieter (K.U.Leuven Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium)

The main result we prove is the following:
Theorem: Suppose that Z_p^h (p prime) acts freely on an n-dimensional torus, then h is less than or equal to n.
This generalizes a result due to Goncalves D.L. and Vieira J.P. who proved the above result in case h is smaller than 4.
The proof boils down to finding an upperbound on the minimal number of generators of Bieberbach group, with an elementary abelian holonomy group. It turns out to be essential to make a difference between the cases p=2 and p > 2.

Date received: January 17, 2006