 
Summary: ON GENERATORS OF CRYSTALLOGRAPHIC GROUPS
AND ACTIONS ON FLAT ORBIFOLDS
A. ADEM
, K. DEKIMPE
, N. PETROSYAN
, AND B. PUTRYCZ
Abstract. We find new bounds on the minimal number of generators
of crystallographic groups with pgroup holonomy. We also show that
similar bounds exist on the minimal number of generators of the abelian
izations of arbitrary crystallographic groups. As a consequence, we show
that this restricts the rank of elementary abelian pgroups that can act
effectively on closed connected flat orbifolds.
1. Introduction
A closed connected flat norbifold M is a quotient of Rn by a cocompact
action of a discrete subgroup of isometries of Rn. A group admitting
such an action is known as a crystallographic group and it is the orbifold
fundamental group of M. When is torsionfree, it is called a Bieberbach
group and it is the fundamental group of the corresponding flat manifold. By
the first Bieberbach theorem (see [2]), every ndimensional crystallographic
group has a normal subgroup T of translations which is a lattice of Rn and
