Duality of finite abelian groups and a Jordan normal form of integer matrices

AbstractLet G be a nonsingular n × n integer matrix. The structure of G is studied using methods from linear systems theory. A group VG ⊂Zn,VG≅ZnGZn is associated to G. A bilinear map (VGVGT) → QZleads to a duality of VG and VGT and to the concept of dual straight bases. If G-1 is equal to the sum of its principal parts then there is a factorization of G which can be considered as the analogue of the transformation of a complex pencil zI - A to Jordan normal form