  The integral monodromy on the Milnor lattice of an isolated quasihomogeneous
singularity is subject of an almost untouched conjecture of Orlik from 1972. We
prove this conjecture for all iterated Thom-Sebastiani sums of chain type
singularities and cycle type singularities. The main part of the paper is
purely algebraic. It provides tools for dealing with sums and tensor products
of ${\mathbb Z}$-lattices with automorphisms of finite order and with cyclic
generators. The calculations are involved. They use fine properties of unit
roots, cyclotomic polynomials, their resultants and discriminants.
