Abstract
In this article, we study the question of whether it is true that an n-dimensional Bieberbach group can be generated by n elements. We answer this question affirmatively in dimension less than or equal to 6, and in case the holonomy group is an elementary abelian p-group.
This result includes an alternative proof for the recent result by Yalçin, saying that whenever an elementary abelian p-group is acting freely on the n-dimensional torus, we must have that h ≤ n.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
Research supported by the Research Grant of the Research Foundation Flanders (FWO): 1.5.026.05, the Research Programmer of the Research Foundation Flanders (FWO): G0570.06, and the Research Fund of the Katholieke Universiteit Leuven.
Notes
Communicated by M. Dixon.