  The groups of (linear) similarity and coincidence isometries of certain
modules in d-dimensional Euclidean space, which naturally occur in
quasicrystallography, are considered. It is shown that the structure of the
factor group of similarity modulo coincidence isometries is the direct sum of
cyclic groups of prime power orders that divide d. In particular, if the
dimension d is a prime number p, the factor group is an elementary Abelian
p-group. This generalizes previous results obtained for lattices to situations
relevant in quasicrystallography.
