ABSTRACT
The starting point of our investigations was the following problem studied by Y. Kitaoka and the first named author around 1978 on the behaviour of the automorphism groups of positive definite quadratic Z-lattices under totally real scalar extensions. There was the
Question. If two positive definite quadratic Z-lattices become isomorphic over the ring OK of integers of a totally real field extension K of the rationals Q, are they already isomorphic over Z, the ring of rational integers?
