Integral filtrations of groups and Magnus theory

In this talk we will give a general setting to classical results of Magnus, Witt, Koch and Lazard and prove new ones. The talk will be devoted to the connection between integral filtrations of the free group, ideals of the integral group ring, ideals of the complete free associative algebra and kernels of homomorphisms from the free group to the ring of upper triangular unipotent matrices. Furthermore, we characterize integral filtrations as powers of the lower central series