  Let K be a principal ideal domain, G a finite group, and M a KG-module which
as K-module is free of finite rank, and on which $G$ acts faithfully. A
generalized crystallographic group (introduced by the authors in volume 5 of
Journal of Group Theory) is a group $\frak C$ which has a normal subgroup
isomorphic to M with quotient G, such that conjugation in $\frak C$ gives the
same action of G on M that we started with. (When $K=\Bbb Z$, these are just
the classical crystallographic groups.) The K-free rank of M is said to be the
dimension of $\frak C$, the holonomy group of $\frak C$ is G, and $\frak C$ is
called indecomposable if M is an indecomposable KG-module.
  Let K be either $\Bbb Z$, or its localization $\Bbb Z_{(p)}$ at the prime p,
or the ring $\Bbb Z_p$ of p-adic integers, and consider indecomposable
torsionfree generalized crystallographic groups whose holonomy group is
noncyclic of order p^2. In Theorem 2, we prove that (for any given p) the
dimensions of these groups are not bounded.
  For $K=\Bbb Z$, we show in Theorem 3 that there are infinitely many
non-isomorphic indecomposable torsionfree crystallographic groups with holonomy
group the alternating group of degree 4. In Theorem 1, we look at a cyclic G
whose order |G| satisfies the following condition: for all prime divisors p of
|G|, p^2 also divides G, and for at least one p, even p^3 does. We prove that
then every product of |G| with a positive integer coprime to it occurs as the
dimension of some indecomposable torsionfree crystallographic group with
holonomy group G.
